The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+76x^78+80x^80+56x^82+6x^84+20x^86+2x^88+2x^92+8x^94+5x^96

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 0.133 seconds.