The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  2  1  2  1  0  0  1  1  2  1  0  0  0  1  1  0  1  2  1  2  0  1  1  0  1  1  0  1  0  1
 0  1  0  0  0  1  1  1  0  0  3  3  1  0  1  1  1  3  0  1  2  1  1  2  0  0  1  1  1  0  0  1  1  1  2  2  2  1  2  1  2  2  0  0
 0  0  1  0  1  1  0  1  0  1  1  2  0  1  1  2  1  1  1  2  0  1  0  2  2  1  1  0  3  1  3  0  1  0  1  2  1  1  1  1  0  3  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  3  0  1  1  1  0  3  3  0  0  2  1  1  2  0  3  3  3  2  1  1  3  1  1  1  0  0  1  1  0  0
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  0  0  2  2  2  0  2  2  0  0  2  0  2  0  2  2  2  2  2  0  2  0  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  2  2  2  0  0  2  0  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  0  0  0  2  2  0  0  0  2  2  0  2  2  0  0  2  2  2  0  2  2  0  0  0  2  2  0  0  2  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  2  2  2  2  0  2  2  2  2  0  0  0  2  0  0  0  2  2  0  0  2  2  2  2  2  0  2  0  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+89x^32+84x^33+189x^34+268x^35+462x^36+500x^37+653x^38+760x^39+921x^40+1108x^41+1149x^42+1330x^43+1225x^44+1346x^45+1217x^46+1216x^47+919x^48+812x^49+695x^50+464x^51+381x^52+216x^53+175x^54+56x^55+83x^56+28x^57+15x^58+2x^59+11x^60+2x^61+3x^62+3x^64+1x^68

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 37.3 seconds.