The generator matrix

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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+256x^66+887x^68+1834x^70+2745x^72+3778x^74+5205x^76+6390x^78+7466x^80+7912x^82+7622x^84+6822x^86+5615x^88+3910x^90+2453x^92+1370x^94+740x^96+316x^98+141x^100+48x^102+14x^104+4x^106+4x^108+1x^112+2x^120

The gray image is a code over GF(2) with n=164, k=16 and d=66.
This code was found by Heurico 1.10 in 630 seconds.