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

generates a code of length 81 over Z4 who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+106x^78+21x^80+84x^82+22x^86+7x^88+10x^90+2x^96+2x^98+1x^104

The gray image is a code over GF(2) with n=162, k=8 and d=78.
This code was found by Heurico 1.16 in 36.9 seconds.