The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 X 1 1
0 X 0 0 0 0 0 0 0 0 0 0 0 0 X 2X 2X X 2X X 2X 0 X 0 2X 2X X 2X 2X 2X 0 2X X X X 0 0 X 0 X 2X 2X X X 2X 2X 2X 2X 2X 2X X X 0 0 2X 2X 2X 2X 2X 0 0 X 2X 0
0 0 X 0 0 0 0 0 0 0 0 X 2X 2X 2X 2X 0 X X 2X 2X X X 2X X 0 0 X 0 2X X X X 0 0 0 2X 2X 2X X 2X X X 0 X 2X X 0 X X X X X 2X 2X 0 2X 2X 2X 0 X 2X X X
0 0 0 X 0 0 0 0 X 2X 2X 2X 0 0 X 0 X 2X 2X 0 2X X 2X X 2X X X X 0 X X 0 2X X X 2X 0 0 X X X 0 0 X X 2X 0 0 0 X 0 X 2X 2X X 0 0 0 X X X 2X X 0
0 0 0 0 X 0 0 X 2X 0 2X 0 0 2X 2X X X X 0 X X 2X X 2X 2X 0 X X X 2X 2X 2X 0 0 0 2X 2X X 2X 2X 0 0 0 0 2X 2X 0 2X 2X 0 X 2X X 2X 2X 2X 2X X 0 X 0 X X 0
0 0 0 0 0 X 0 2X 2X X 0 2X 2X 2X 2X 2X 2X 0 0 X 0 2X 2X 2X X 2X 0 2X X X X 0 0 0 0 0 0 X 0 2X 0 2X 2X X 0 0 X 0 0 X 2X X 0 0 2X X 2X 2X 2X X X 2X 2X 2X
0 0 0 0 0 0 X 2X 2X 2X 2X 2X 2X X X X 0 2X X 2X 2X 2X 2X 0 X 2X X X X 2X 2X X X 2X X X 2X X X 2X 0 0 X 2X 0 X 0 X 2X 0 2X 2X 0 0 0 X 2X 0 0 0 0 0 2X 2X
generates a code of length 64 over Z3[X]/(X^2) who´s minimum homogenous weight is 111.
Homogenous weight enumerator: w(x)=1x^0+106x^111+174x^114+232x^117+264x^120+658x^123+1486x^126+1912x^129+1050x^132+156x^135+132x^138+122x^141+128x^144+58x^147+46x^150+18x^153+12x^156+2x^159+2x^162+2x^180
The gray image is a linear code over GF(3) with n=192, k=8 and d=111.
This code was found by Heurico 1.16 in 1.28 seconds.