The generator matrix

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

generates a code of length 51 over Z4 who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+68x^38+346x^40+756x^42+1142x^44+1604x^46+1950x^48+2244x^50+2352x^52+2086x^54+1669x^56+1098x^58+608x^60+294x^62+113x^64+38x^66+10x^68+4x^70+1x^72

The gray image is a code over GF(2) with n=102, k=14 and d=38.
This code was found by Heurico 1.10 in 9.7 seconds.