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.