The generator matrix

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

generates a code of length 88 over Z4 who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+64x^79+106x^80+114x^81+135x^82+144x^83+151x^84+128x^85+136x^86+116x^87+133x^88+120x^89+81x^90+84x^91+81x^92+86x^93+40x^94+54x^95+44x^96+32x^97+34x^98+30x^99+34x^100+18x^101+17x^102+14x^103+20x^104+14x^105+2x^106+6x^107+2x^108+3x^110+4x^112

The gray image is a code over GF(2) with n=176, k=11 and d=79.
This code was found by Heurico 1.10 in 0.296 seconds.