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

generates a code of length 58 over Z3[X]/(X^3) who´s minimum homogenous weight is 111.

Homogenous weight enumerator: w(x)=1x^0+56x^111+48x^112+192x^114+60x^115+1620x^116+32x^117+18x^118+74x^120+24x^121+48x^123+12x^124+2x^174

The gray image is a linear code over GF(3) with n=522, k=7 and d=333.
This code was found by Heurico 1.16 in 0.102 seconds.