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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+38x^64+60x^65+158x^66+228x^67+267x^68+314x^69+356x^70+378x^71+384x^72+362x^73+440x^74+496x^75+407x^76+474x^77+454x^78+474x^79+462x^80+402x^81+371x^82+332x^83+306x^84+260x^85+193x^86+162x^87+137x^88+104x^89+65x^90+40x^91+40x^92+8x^93+8x^94+2x^95+6x^96+2x^98+1x^110

The gray image is a code over GF(2) with n=154, k=13 and d=64.
This code was found by Heurico 1.10 in 4.49 seconds.