The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+30x^78+64x^79+30x^80+1x^94+1x^96+1x^126

The gray image is a code over GF(2) with n=158, k=7 and d=78.
This code was found by Heurico 1.16 in 0.116 seconds.