The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+42x^73+136x^74+234x^75+431x^76+512x^77+659x^78+760x^79+904x^80+1032x^81+1207x^82+1326x^83+1432x^84+1574x^85+1643x^86+1764x^87+1757x^88+1816x^89+1767x^90+1802x^91+1657x^92+1676x^93+1541x^94+1312x^95+1234x^96+1040x^97+865x^98+778x^99+594x^100+414x^101+301x^102+196x^103+165x^104+86x^105+73x^106+20x^107+14x^108+2x^112+1x^160

The gray image is a code over GF(2) with n=178, k=15 and d=73.
This code was found by Heurico 1.10 in 160 seconds.