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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 108.

Homogenous weight enumerator: w(x)=1x^0+50x^108+160x^111+54x^113+86x^114+270x^116+98x^117+486x^119+90x^120+432x^122+28x^123+216x^125+52x^126+38x^129+28x^132+34x^135+28x^138+20x^141+8x^144+4x^147+2x^156+2x^165

The gray image is a linear code over GF(3) with n=180, k=7 and d=108.
This code was found by Heurico 1.16 in 0.15 seconds.