The generator matrix

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

generates a code of length 82 over Z4 who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+144x^70+475x^72+633x^74+801x^76+831x^78+840x^80+934x^82+819x^84+783x^86+707x^88+515x^90+345x^92+219x^94+87x^96+30x^98+19x^100+7x^102+2x^104

The gray image is a code over GF(2) with n=164, k=13 and d=70.
This code was found by Heurico 1.10 in 4.97 seconds.