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

generates a code of length 51 over Z3[X]/(X^2) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+138x^78+384x^81+642x^84+952x^87+1314x^90+3050x^93+5540x^96+10362x^99+12684x^102+11602x^105+6672x^108+2720x^111+1320x^114+816x^117+448x^120+202x^123+132x^126+54x^129+8x^132+2x^135+4x^138+2x^141

The gray image is a linear code over GF(3) with n=153, k=10 and d=78.
This code was found by Heurico 1.16 in 67.9 seconds.