The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+141x^32+46x^34+518x^36+462x^38+1096x^40+1036x^42+1576x^44+1020x^46+1170x^48+454x^50+481x^52+54x^54+120x^56+16x^60+1x^84

The gray image is a code over GF(2) with n=88, k=13 and d=32.
This code was found by Heurico 1.16 in 6.21 seconds.