The generator matrix

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

generates a code of length 87 over Z4 who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+58x^73+196x^74+258x^75+317x^76+424x^77+544x^78+582x^79+595x^80+738x^81+729x^82+772x^83+823x^84+832x^85+907x^86+858x^87+918x^88+924x^89+904x^90+788x^91+701x^92+664x^93+554x^94+570x^95+422x^96+338x^97+285x^98+228x^99+165x^100+112x^101+91x^102+38x^103+23x^104+6x^105+14x^106+2x^107+2x^108+1x^136

The gray image is a code over GF(2) with n=174, k=14 and d=73.
This code was found by Heurico 1.10 in 20.1 seconds.