The generator matrix

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

generates a code of length 49 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+114x^78+298x^81+24x^83+554x^84+114x^85+252x^86+1372x^87+420x^88+666x^89+2228x^90+1122x^91+1332x^92+4172x^93+2094x^94+2574x^95+6004x^96+3156x^97+3042x^98+6874x^99+3102x^100+2934x^101+5602x^102+2166x^103+1548x^104+3148x^105+798x^106+666x^107+1454x^108+150x^109+84x^110+524x^111+252x^114+128x^117+56x^120+18x^123+6x^126

The gray image is a linear code over GF(3) with n=147, k=10 and d=78.
This code was found by Heurico 1.16 in 38.1 seconds.