The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+96x^32+196x^33+343x^34+530x^35+809x^36+1036x^37+1205x^38+1446x^39+1966x^40+2224x^41+2299x^42+2716x^43+2702x^44+2640x^45+2599x^46+2434x^47+2037x^48+1624x^49+1193x^50+902x^51+737x^52+400x^53+255x^54+150x^55+92x^56+68x^57+37x^58+12x^59+8x^60+4x^61+5x^62+2x^63

The gray image is a code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.10 in 31.8 seconds.