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  1  1  1  1  1  1  1  1  1  1  0  1  X  1  1  1  1  1  1  1
 0  X  0  0 2X 2X^2+X 2X^2+2X  X 2X X^2  X  X 2X^2+2X 2X^2+X  0 X^2 2X^2+2X 2X X^2 2X^2+X X^2 2X^2 2X^2+2X 2X^2+X  X 2X X^2+2X X^2 X^2+X 2X^2+2X 2X^2 2X^2+X 2X^2+2X X^2 X^2+X 2X^2+X 2X^2+2X 2X^2 X^2+2X  X  X X^2+2X X^2+2X 2X^2  0 X^2 2X 2X^2 X^2+X  0  X 2X 2X^2 X^2+2X X^2+X 2X X^2 2X X^2+X
 0  0  X 2X X^2 2X^2+2X X^2+X  X 2X^2+2X 2X^2 X^2+X 2X^2 X^2+X 2X  X 2X  0 2X 2X^2 2X^2 X^2+2X 2X^2+X  0 2X^2+2X X^2+X X^2+X X^2+2X X^2+2X X^2+2X  X  X  X X^2 X^2 X^2 X^2+X 2X^2+2X 2X 2X^2+X X^2 X^2 2X X^2  X 2X^2+X 2X^2+X X^2+2X  0 2X^2+2X  X  X 2X^2 X^2+2X 2X^2+2X 2X^2+X  0 X^2  0 2X^2+2X
 0  0  0 X^2  0  0 2X^2 X^2 2X^2 2X^2 2X^2 X^2 X^2 2X^2 X^2 2X^2 2X^2 X^2 X^2 2X^2  0 2X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0  0  0 2X^2  0  0 X^2 X^2 X^2  0 2X^2 X^2  0 2X^2 X^2 2X^2  0 X^2  0 2X^2  0 2X^2 2X^2 2X^2 X^2 X^2  0  0

generates a code of length 59 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+348x^111+534x^114+648x^116+734x^117+1944x^118+1296x^119+548x^120+174x^123+154x^126+128x^129+48x^132+2x^138+2x^171

The gray image is a linear code over GF(3) with n=531, k=8 and d=333.
This code was found by Heurico 1.16 in 0.401 seconds.