The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+84x^72+180x^74+216x^76+148x^78+105x^80+62x^82+71x^84+50x^86+29x^88+20x^90+23x^92+14x^94+13x^96+6x^98+2x^100

The gray image is a code over GF(2) with n=158, k=10 and d=72.
This code was found by Heurico 1.16 in 0.247 seconds.