The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 31.

Homogenous weight enumerator: w(x)=1x^0+20x^31+119x^32+236x^33+386x^34+562x^35+765x^36+1028x^37+1260x^38+1594x^39+1815x^40+2052x^41+2362x^42+2564x^43+2687x^44+2776x^45+2626x^46+2184x^47+2018x^48+1704x^49+1245x^50+930x^51+657x^52+448x^53+274x^54+186x^55+109x^56+72x^57+38x^58+24x^59+19x^60+4x^61+2x^64+1x^66

The gray image is a code over GF(2) with n=88, k=15 and d=31.
This code was found by Heurico 1.10 in 30.4 seconds.