The generator matrix
1 0 1 1 1 1 1 0 1 1 1 0 1 1 1 0 X 1 1 1 1 1 1 0 1 1 0 1 1 1 2X 1 1 0 1 1 1 X 2X 1 X 1 1 2X 1 1 1 1 2X 1 1 1 1 X 1 X 0 1 1 1 1 1 1 0 1 1 1 1 1
0 1 1 2 0 1 2 1 0 2X+1 2 1 0 2 2X+1 1 1 X+2 0 2X+1 0 2X+1 2 1 0 2 1 2X+1 0 2X+1 1 1 X 1 2X+1 2 1 1 1 2X 1 2X+2 X+2 1 2X+1 X 2X+1 2X+1 1 2 2X+2 X+2 2X+1 1 0 1 1 2 X+1 X+2 X 0 X+1 1 X+1 0 0 0 0
0 0 2X 0 0 0 0 0 0 2X X 2X 2X 2X 2X 0 2X 0 2X 2X 0 2X 2X 0 2X 0 0 X 2X X 0 X 0 2X 2X 0 X 2X 2X X 2X X X X 0 0 X 2X 0 X 0 0 2X X X 2X 2X 2X 0 2X 0 0 2X 0 X 2X 2X 0 0
0 0 0 X 0 0 0 0 0 0 0 0 0 0 2X X 2X X 0 X X 2X 2X X 0 0 X X X 2X X 2X X 0 X 2X 2X 2X X 2X X X X 2X 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 X X 0 2X 0 X 0 0 2X X 2X 0
0 0 0 0 X 0 0 0 0 0 0 0 0 0 2X 2X X 0 2X X 2X 0 2X X 2X 2X 2X 2X X 2X 0 2X X X 2X 0 2X 0 0 0 0 2X 0 X 2X X X 0 X 2X 2X X 2X X X 0 2X X X X X 2X 0 0 0 X 0 0 0
0 0 0 0 0 2X 0 0 X 2X 2X X 2X 0 2X 2X 2X X 0 0 0 X X X 0 X 2X 0 0 X 0 2X 2X 0 0 2X 0 2X X 0 X 2X 2X X 2X 2X 0 0 2X X 0 2X 0 X 2X 0 2X X X X X 0 0 X X 0 X X 0
0 0 0 0 0 0 X 0 X 0 X X X 2X 2X 0 X 2X 2X 0 2X X 2X 0 0 X X X 2X 0 0 2X 0 X 2X 2X 0 0 2X 0 2X 2X 0 0 2X 2X X X 0 2X 0 2X X 0 0 2X X X 2X 2X X 2X 0 0 0 0 2X 0 0
0 0 0 0 0 0 0 X X X X 0 2X X 2X X X X X 2X 2X 2X X 0 X X 0 2X 2X 2X X X 2X 0 0 2X 0 X X X 2X 0 2X 0 X 2X X X X X 2X 0 2X 2X X 0 X X 2X X X 0 X 0 X 2X X 2X 0
generates a code of length 69 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.
Homogenous weight enumerator: w(x)=1x^0+46x^114+206x^117+460x^120+1016x^123+2116x^126+3864x^129+6176x^132+9370x^135+11160x^138+10212x^141+7412x^144+4132x^147+1630x^150+626x^153+264x^156+178x^159+106x^162+42x^165+20x^168+8x^171+4x^174
The gray image is a linear code over GF(3) with n=207, k=10 and d=114.
This code was found by Heurico 1.16 in 60.3 seconds.