The generator matrix

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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+97x^64+468x^66+983x^68+1780x^70+2707x^72+3870x^74+5173x^76+6276x^78+7437x^80+7636x^82+7525x^84+6664x^86+5343x^88+3828x^90+2675x^92+1524x^94+853x^96+384x^98+196x^100+76x^102+26x^104+6x^106+8x^108

The gray image is a code over GF(2) with n=164, k=16 and d=64.
This code was found by Heurico 1.10 in 628 seconds.