The generator matrix

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

generates a code of length 79 over Z4 who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+95x^64+146x^65+292x^66+492x^67+589x^68+742x^69+831x^70+1022x^71+1149x^72+1284x^73+1509x^74+1632x^75+1778x^76+1846x^77+1912x^78+1978x^79+1951x^80+1822x^81+1828x^82+1774x^83+1527x^84+1402x^85+1234x^86+1022x^87+785x^88+632x^89+471x^90+336x^91+274x^92+170x^93+102x^94+58x^95+35x^96+20x^97+12x^98+6x^99+8x^100+1x^134

The gray image is a code over GF(2) with n=158, k=15 and d=64.
This code was found by Heurico 1.10 in 142 seconds.