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.