The generator matrix

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

generates a code of length 58 over Z3[X]/(X^2) who´s minimum homogenous weight is 112.

Homogenous weight enumerator: w(x)=1x^0+120x^112+138x^113+46x^114+102x^115+120x^116+66x^118+24x^119+12x^120+6x^121+24x^122+20x^123+12x^125+2x^126+12x^127+6x^130+6x^131+12x^133

The gray image is a linear code over GF(3) with n=174, k=6 and d=112.
This code was found by Heurico 1.16 in 0.0435 seconds.