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.