The generator matrix

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

generates a code of length 68 over Z4 who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+30x^51+78x^52+158x^53+276x^54+510x^55+684x^56+860x^57+1217x^58+1582x^59+1819x^60+2118x^61+2528x^62+3054x^63+3408x^64+3540x^65+3944x^66+4288x^67+4464x^68+4406x^69+4285x^70+3956x^71+3532x^72+3192x^73+2793x^74+2258x^75+1728x^76+1418x^77+1050x^78+774x^79+513x^80+372x^81+243x^82+158x^83+142x^84+60x^85+45x^86+26x^87+14x^88+4x^89+2x^90+4x^91+1x^92+1x^98

The gray image is a code over GF(2) with n=136, k=16 and d=51.
This code was found by Heurico 1.10 in 465 seconds.