The generator matrix

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

generates a code of length 64 over Z4 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+80x^53+196x^54+238x^55+300x^56+368x^57+380x^58+428x^59+431x^60+528x^61+462x^62+422x^63+504x^64+498x^65+555x^66+452x^67+487x^68+414x^69+323x^70+314x^71+253x^72+190x^73+114x^74+120x^75+62x^76+34x^77+15x^78+10x^79+9x^80+2x^82+1x^90+1x^96

The gray image is a code over GF(2) with n=128, k=13 and d=53.
This code was found by Heurico 1.10 in 26.2 seconds.