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

generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+104x^72+370x^75+608x^78+820x^81+1086x^84+270x^85+1474x^87+1620x^88+1814x^90+4860x^91+2138x^93+9990x^94+2286x^96+12474x^97+2432x^99+7776x^100+2040x^102+2376x^103+1786x^105+1162x^108+756x^111+452x^114+202x^117+88x^120+36x^123+26x^126+2x^129

The gray image is a linear code over GF(3) with n=144, k=10 and d=72.
This code was found by Heurico 1.16 in 61.8 seconds.