The generator matrix

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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+51x^72+110x^73+112x^74+142x^75+136x^76+134x^77+149x^78+150x^79+131x^80+108x^81+101x^82+82x^83+85x^84+74x^85+66x^86+72x^87+76x^88+52x^89+28x^90+36x^91+47x^92+24x^93+21x^94+24x^95+13x^96+10x^97+3x^98+4x^99+4x^100+2x^103

The gray image is a code over GF(2) with n=162, k=11 and d=72.
This code was found by Heurico 1.16 in 0.777 seconds.