The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+194x^72+270x^74+349x^76+220x^78+247x^80+148x^82+198x^84+132x^86+78x^88+94x^90+61x^92+24x^94+14x^96+8x^98+8x^100+2x^104

The gray image is a code over GF(2) with n=160, k=11 and d=72.
This code was found by Heurico 1.16 in 2.53 seconds.