The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+184x^64+616x^66+990x^68+1322x^70+1484x^72+1744x^74+1887x^76+1844x^78+1810x^80+1516x^82+1260x^84+900x^86+469x^88+226x^90+101x^92+22x^94+3x^96+2x^98+2x^100+1x^120

The gray image is a code over GF(2) with n=154, k=14 and d=64.
This code was found by Heurico 1.10 in 17.3 seconds.