The generator matrix
1 0 0 1 1 1 1 1 0 2X 1 1 1 1 1 2X 1 X 1 1 1 0 1 1 1 0 1 1 1 1 0 1 2X 0 1 1 2X 1 1 1 1 X 1 1 1 1 1 1
0 1 0 1 0 2 1 2 1 1 0 2X+1 2X+2 2X+1 1 1 2 1 2 2X 0 1 X+2 2X+1 X+1 0 X 2X 0 2X+1 1 2 1 1 X+2 1 2X 2X+2 2 2X+1 X 1 2X 2X 2X+1 X+2 2 0
0 0 1 2 1 2 1 0 2 2X+1 2 2X 2X+1 2X+2 1 X+1 2 X 2X 1 2 2X+2 X+1 0 X+2 1 X X+1 X 0 2X+1 2 2 0 2X 2X 1 X+1 X+1 2X+1 X+1 X X 2X+1 2X 1 0 0
0 0 0 2X 0 0 0 0 0 0 0 0 0 2X X X 2X X X X 2X X 2X X 2X X 0 2X 2X 2X 2X 0 0 2X X 2X 2X 0 0 0 2X X X 2X 2X 0 0 0
0 0 0 0 2X 0 0 0 0 0 X 2X 2X 2X 2X X X X X 0 X 2X 0 0 2X 2X X 2X 0 2X 0 X X 2X X 0 0 X X X X 0 0 X 2X 0 X 0
0 0 0 0 0 X 0 X X 2X 2X 2X 2X 2X 2X 0 2X X 0 X 2X 2X 0 2X X X 2X X X 0 X X 0 X 2X 2X X 2X 0 0 X 0 X X 2X X 2X 0
0 0 0 0 0 0 X X X X X 2X X 2X 0 X 0 2X X X 2X 2X X X 2X 2X 0 X X X X 0 0 X X X 2X 0 2X X 2X 0 0 0 0 2X X 0
generates a code of length 48 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.
Homogenous weight enumerator: w(x)=1x^0+62x^78+12x^79+18x^80+384x^81+180x^82+348x^83+918x^84+510x^85+636x^86+2148x^87+1002x^88+1098x^89+3624x^90+1788x^91+2076x^92+5244x^93+2334x^94+2640x^95+6892x^96+2730x^97+2682x^98+6378x^99+2418x^100+2058x^101+4332x^102+1452x^103+1092x^104+1898x^105+576x^106+414x^107+622x^108+96x^109+54x^110+186x^111+24x^112+6x^113+64x^114+32x^117+12x^120+6x^123+2x^126
The gray image is a linear code over GF(3) with n=144, k=10 and d=78.
This code was found by Heurico 1.16 in 31.8 seconds.