The generator matrix

1 0 0 0 0 0 0 1 1 1 2 1 1 1 1 1 2 1 1 2 1 2 2 2 0 1 0 1 0 1 1 1 1 2 0 1 2 1 2 1 0 1 1 2 0 1 1 2 1 1 2 2 1 0 0 2 1 1 2 2 0 0 2 0 2 0 0 1 1 2 0 1 1 2 1 2 2 1 0 2 2 1 0 1 0 1 1 1
0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 1 3 1 3 1 1 3 1 3 1 1 1 3 3 1 1 1 0 2 2 0 1 0 3 2 1 1 2 3 0 0 1 1 2 1 2 1 0 3 2 1 1 1 3 2 3 2 0 0 1 1 0 3 1 2 2 2 3 0
0 0 1 0 0 0 0 0 0 0 0 0 1 1 1 3 1 1 2 1 2 0 1 1 1 2 1 3 0 3 2 2 3 3 1 3 0 1 2 3 3 3 3 2 1 0 1 1 0 1 1 1 2 0 0 1 3 1 1 1 0 1 1 0 0 1 1 3 2 3 0 0 0 1 3 2 1 3 2 3 2 3 1 0 2 0 1 0
0 0 0 1 0 0 0 0 0 0 0 1 0 2 2 1 1 1 3 3 1 1 0 1 2 3 2 1 1 0 3 0 1 3 0 3 3 0 0 1 2 2 1 3 0 3 2 3 1 3 0 3 2 1 1 2 3 2 0 0 0 0 0 3 1 1 2 0 1 3 1 0 1 2 1 1 2 1 0 0 1 1 1 3 1 2 2 0
0 0 0 0 1 0 0 0 1 1 1 2 2 0 1 1 1 3 2 0 3 0 2 3 3 1 1 2 3 3 1 2 0 0 3 3 1 0 3 0 2 3 1 0 2 3 3 2 2 2 1 0 2 3 1 3 1 0 0 2 3 0 3 3 0 3 0 3 2 2 1 1 1 0 3 1 0 0 0 1 3 0 1 1 2 3 0 0
0 0 0 0 0 1 0 1 0 1 3 2 2 1 3 2 2 3 1 3 2 1 3 3 3 3 0 3 1 2 2 3 0 3 3 0 2 1 3 1 3 2 1 3 0 2 3 1 0 2 1 2 1 2 3 2 3 3 0 1 0 3 0 3 3 2 0 2 1 0 0 3 1 2 2 1 0 3 2 0 1 2 2 0 2 2 0 0
0 0 0 0 0 0 1 1 3 2 1 1 3 0 1 3 0 0 0 0 2 1 1 3 0 1 3 3 2 2 3 2 1 1 1 0 2 3 0 2 0 3 1 1 2 0 2 3 2 3 2 0 3 0 0 1 3 0 1 2 0 3 0 3 1 3 1 3 1 1 3 1 3 2 2 1 3 1 3 3 2 0 0 0 1 0 1 0
0 0 0 0 0 0 0 2 2 0 2 2 2 0 2 2 0 0 0 0 0 2 2 2 0 2 2 2 0 0 2 0 2 2 2 0 0 2 0 0 0 2 2 0 2 2 2 0 2 0 2 2 0 2 2 0 0 2 0 2 2 0 2 0 0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 2 0 0 0 0 0 0

generates a code of length 88 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+73x^72+94x^73+295x^74+394x^75+570x^76+628x^77+759x^78+878x^79+1028x^80+1276x^81+1266x^82+1454x^83+1559x^84+1638x^85+1787x^86+1780x^87+1702x^88+1844x^89+1699x^90+1758x^91+1630x^92+1426x^93+1357x^94+1264x^95+1063x^96+916x^97+766x^98+540x^99+459x^100+312x^101+209x^102+118x^103+93x^104+52x^105+53x^106+6x^107+14x^108+4x^109+2x^113+1x^154

The gray image is a code over GF(2) with n=176, k=15 and d=72.
This code was found by Heurico 1.10 in 162 seconds.