The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+112x^32+188x^33+330x^34+568x^35+736x^36+1040x^37+1190x^38+1550x^39+1903x^40+2124x^41+2519x^42+2630x^43+2662x^44+2744x^45+2599x^46+2280x^47+2075x^48+1592x^49+1224x^50+992x^51+604x^52+452x^53+300x^54+154x^55+85x^56+48x^57+23x^58+18x^59+14x^60+4x^61+7x^62

The gray image is a code over GF(2) with n=88, k=15 and d=32.
This code was found by Heurico 1.16 in 79.5 seconds.