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

generates a code of length 77 over Z4 who´s minimum homogenous weight is 65.

Homogenous weight enumerator: w(x)=1x^0+60x^65+149x^66+212x^67+277x^68+336x^69+353x^70+392x^71+407x^72+424x^73+399x^74+472x^75+454x^76+432x^77+484x^78+428x^79+468x^80+398x^81+425x^82+330x^83+261x^84+266x^85+208x^86+174x^87+97x^88+118x^89+83x^90+34x^91+16x^92+14x^93+10x^94+6x^95+2x^96+1x^102+1x^112

The gray image is a code over GF(2) with n=154, k=13 and d=65.
This code was found by Heurico 1.10 in 4.56 seconds.