The generator matrix

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

generates a code of length 65 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+64x^51+197x^52+344x^53+420x^54+590x^55+825x^56+932x^57+1200x^58+1282x^59+1490x^60+1776x^61+1817x^62+2002x^63+2139x^64+2264x^65+2258x^66+2052x^67+1973x^68+1944x^69+1614x^70+1310x^71+1157x^72+938x^73+690x^74+534x^75+332x^76+220x^77+161x^78+98x^79+70x^80+24x^81+23x^82+4x^83+8x^84+4x^85+4x^86+2x^89+4x^90+1x^98

The gray image is a code over GF(2) with n=130, k=15 and d=51.
This code was found by Heurico 1.10 in 110 seconds.