The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+13x^32+114x^33+189x^34+282x^35+442x^36+554x^37+667x^38+780x^39+923x^40+1082x^41+1186x^42+1230x^43+1287x^44+1304x^45+1188x^46+1146x^47+1089x^48+854x^49+678x^50+476x^51+311x^52+230x^53+160x^54+106x^55+24x^56+22x^57+23x^58+12x^59+4x^60+5x^62+2x^64

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.10 in 7.88 seconds.