The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+25x^72+88x^73+141x^74+296x^75+374x^76+416x^77+470x^78+560x^79+649x^80+680x^81+739x^82+758x^83+842x^84+852x^85+923x^86+916x^87+845x^88+882x^89+874x^90+798x^91+709x^92+658x^93+565x^94+544x^95+461x^96+314x^97+308x^98+214x^99+154x^100+122x^101+70x^102+68x^103+31x^104+20x^105+6x^106+6x^107+4x^108+1x^132

The gray image is a code over GF(2) with n=174, k=14 and d=72.
This code was found by Heurico 1.10 in 19.8 seconds.