The generator matrix

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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 113.

Homogenous weight enumerator: w(x)=1x^0+252x^113+154x^114+366x^116+212x^117+282x^119+128x^120+132x^122+86x^123+216x^125+60x^126+114x^128+44x^129+48x^131+12x^132+30x^134+24x^135+18x^137+6x^138+2x^147

The gray image is a linear code over GF(3) with n=180, k=7 and d=113.
This code was found by Heurico 1.13 in 0.067 seconds.