The generator matrix

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

generates a code of length 67 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+40x^51+152x^52+284x^53+481x^54+688x^55+916x^56+1200x^57+1476x^58+1828x^59+2187x^60+2528x^61+3007x^62+3462x^63+3723x^64+4042x^65+4160x^66+4360x^67+4386x^68+4312x^69+4142x^70+3532x^71+3183x^72+2680x^73+2232x^74+1800x^75+1347x^76+1036x^77+739x^78+562x^79+414x^80+262x^81+124x^82+100x^83+61x^84+32x^85+23x^86+12x^87+11x^88+8x^89+2x^92+1x^100

The gray image is a code over GF(2) with n=134, k=16 and d=51.
This code was found by Heurico 1.10 in 479 seconds.