The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  2  1  2  2  1  0  1  2  1  1  2  2  1  0  2  2  1  0  1  1  2  0  0  0  1  1  1
 0  2  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  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  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  2  2
 0  0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  0  2  2  0  0  2  2  2  2  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  0  2  0  0  2  0  2  2  0  0  0  0  2  2  0  2  2  2  0  2  2  0  0
 0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  2  2  2  0  0  2  0  2  2  0  2  2  0
 0  0  0  0  2  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  0  0  2  2  2  2  2  2  2
 0  0  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  0  2  2  2  0  0  0  0  0  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  0  2  2  0

generates a code of length 80 over Z4 who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+40x^77+25x^78+25x^80+24x^85+6x^86+6x^88+1x^126

The gray image is a code over GF(2) with n=160, k=7 and d=77.
This code was found by Heurico 1.16 in 9.63 seconds.