The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 114.

Homogenous weight enumerator: w(x)=1x^0+36x^114+162x^116+24x^117+16x^120+2x^135+2x^147

The gray image is a linear code over GF(3) with n=174, k=5 and d=114.
This code was found by Heurico 1.16 in 0.0201 seconds.