The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+53x^76+68x^78+56x^80+44x^82+13x^84+6x^86+1x^88+4x^90+4x^94+2x^102+2x^104+2x^108

The gray image is a code over GF(2) with n=160, k=8 and d=76.
This code was found by Heurico 1.16 in 0.102 seconds.