The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  1  1  2  2  2  2  2  2  1  1  1  2  2  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  2  2  2  2  2  2  2  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  0  2  2  2  0  2  2  2  0  2  2  0  2  2  0  0  2  0  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  0  0  2  0  2  2  2  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  2  0  2  2  0  0  2  0  2  0  2  0  2  0  2  2  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  2  0  2  2  0  2  2  2  0  0  0  2  0  0  0  0  2  2  0  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  2  2  0  0  0  2  2  0  0  2  2  2  0  2  2  0  2  2  2  0  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  0  0  0  2  0  0  2  2  0

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

Homogenous weight enumerator: w(x)=1x^0+58x^32+43x^34+2x^35+104x^36+18x^37+71x^38+72x^39+107x^40+168x^41+89x^42+252x^43+98x^44+252x^45+104x^46+168x^47+69x^48+72x^49+93x^50+18x^51+52x^52+2x^53+76x^54+21x^56+31x^58+2x^60+4x^62+1x^70

The gray image is a code over GF(2) with n=88, k=11 and d=32.
This code was found by Heurico 1.16 in 0.504 seconds.