The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+122x^38+126x^39+334x^40+456x^41+733x^42+752x^43+1139x^44+1396x^45+1502x^46+1840x^47+1849x^48+2306x^49+2382x^50+2490x^51+2419x^52+2420x^53+2122x^54+2014x^55+1737x^56+1360x^57+1020x^58+700x^59+579x^60+328x^61+256x^62+132x^63+116x^64+54x^65+48x^66+10x^67+15x^68+6x^70+3x^72+1x^74

The gray image is a code over GF(2) with n=102, k=15 and d=38.
This code was found by Heurico 1.10 in 37.5 seconds.