The generator matrix

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

generates a code of length 51 over Z4 who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+22x^37+78x^38+192x^39+313x^40+488x^41+656x^42+844x^43+1067x^44+1258x^45+1518x^46+1784x^47+2077x^48+2276x^49+2469x^50+2496x^51+2434x^52+2350x^53+2090x^54+2000x^55+1647x^56+1306x^57+1086x^58+732x^59+555x^60+414x^61+270x^62+120x^63+98x^64+72x^65+21x^66+24x^67+4x^69+4x^70+2x^73

The gray image is a code over GF(2) with n=102, k=15 and d=37.
This code was found by Heurico 1.10 in 37.6 seconds.