The generator matrix

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

generates a code of length 80 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+207x^64+858x^66+1667x^68+2706x^70+4014x^72+5090x^74+6496x^76+7534x^78+7899x^80+7778x^82+6881x^84+5512x^86+3891x^88+2478x^90+1329x^92+726x^94+334x^96+68x^98+42x^100+18x^102+5x^104+1x^112+1x^124

The gray image is a code over GF(2) with n=160, k=16 and d=64.
This code was found by Heurico 1.10 in 621 seconds.