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  3  1  1  1  1  3  3  1  3  3  3  3  3  3  1  1  1
 0  3  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  6  3  6  3  6  3  6  6  3  6  6  6  3  3  3  3  6  3  3  0  3  6  3  3  3  0  3  3  0  3  0
 0  0  3  0  0  0  0  0  0  0  0  0  0  0  0  6  3  6  6  6  3  3  3  3  0  3  3  6  0  3  6  0  6  0  3  3  0  6  6  3  6  3  0  0  3  3  0  6  0  3  3
 0  0  0  3  0  0  0  0  0  0  0  0  3  3  3  6  6  3  6  0  3  0  0  3  6  6  0  6  0  6  3  6  6  3  0  0  0  0  6  3  6  6  0  6  6  6  6  6  0  6  3
 0  0  0  0  3  0  0  0  0  0  3  3  6  6  3  3  6  6  6  3  3  6  0  3  3  3  6  0  6  6  6  0  3  0  3  6  6  0  0  3  0  6  3  6  6  3  6  6  3  6  3
 0  0  0  0  0  3  0  0  0  3  6  6  6  3  3  6  6  6  3  0  0  6  3  6  6  6  3  3  3  3  6  3  0  3  0  6  0  0  3  0  6  3  3  3  0  0  0  6  0  0  6
 0  0  0  0  0  0  3  0  0  6  6  3  3  0  3  3  3  0  0  6  0  0  0  6  6  3  0  6  6  0  0  3  6  0  6  3  6  0  6  3  6  6  0  0  0  6  6  3  3  0  3
 0  0  0  0  0  0  0  3  0  6  3  6  3  6  0  0  6  6  6  0  6  6  6  0  3  0  3  3  3  6  0  0  0  0  6  6  3  6  0  0  3  0  0  6  6  3  6  0  6  0  6
 0  0  0  0  0  0  0  0  3  3  0  3  0  3  6  0  6  6  0  3  3  3  0  6  6  3  6  6  3  3  3  6  6  6  0  6  0  0  3  6  0  0  3  0  3  0  0  6  6  6  3

generates a code of length 51 over Z9 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 code over GF(3) with n=153, k=10 and d=78.
This code was found by Heurico 1.16 in 68.3 seconds.