The generator matrix

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

generates a code of length 89 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+116x^72+154x^73+374x^74+568x^75+739x^76+956x^77+1215x^78+1448x^79+1597x^80+1954x^81+2238x^82+2536x^83+2857x^84+3244x^85+3396x^86+3578x^87+3721x^88+3786x^89+3666x^90+3668x^91+3680x^92+3314x^93+3033x^94+2708x^95+2287x^96+1928x^97+1676x^98+1316x^99+1034x^100+828x^101+626x^102+454x^103+281x^104+188x^105+148x^106+104x^107+65x^108+26x^109+10x^110+4x^111+4x^112+6x^113+2x^114+1x^116+1x^144

The gray image is a code over GF(2) with n=178, k=16 and d=72.
This code was found by Heurico 1.13 in 317 seconds.