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

generates a code of length 60 over Z3[X]/(X^2) who´s minimum homogenous weight is 102.

Homogenous weight enumerator: w(x)=1x^0+48x^102+148x^105+206x^108+18x^110+218x^111+180x^113+228x^114+720x^116+220x^117+1440x^119+206x^120+1440x^122+186x^123+576x^125+166x^126+140x^129+152x^132+112x^135+76x^138+36x^141+18x^144+12x^147+6x^150+6x^153+2x^165

The gray image is a linear code over GF(3) with n=180, k=8 and d=102.
This code was found by Heurico 1.16 in 1.14 seconds.