The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  0  2  1  1  1  1  0  0  1  1  0  0  1  2  2  1  0  1  0  1  2  2  1  2  1  1  1  2  1  1  2
 0  1  0  1  0  1  1  0  0  1  1  1  1  2  1  2  3  0  1  1  0  0  1  0  0  2  1  1  0  1  1  1  0  0  1  3  1  0  2  3  0  3  3  0
 0  0  1  1  1  0  1  0  1  1  0  2  3  1  1  1  0  0  3  0  1  0  3  1  1  1  1  2  0  3  2  0  3  1  1  2  2  3  0  3  1  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  2  0  2  0  0  0  2  0  0  0  2  0  0  2  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0
 0  0  0  0  2  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  0  2  2  2  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  0  2  0  0  2  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  0  2  0  0  0  0  2  0  0  2  0  2  2
 0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  0  0  2  0  0  2  0  2  0  2  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  0  2  0  2  2  0  2  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  0  0  0  0  0  0  2  2
 0  0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  0  2  0  2  0  2  0  2  0  2  0  0  0  2  2  2  2  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+157x^32+274x^34+820x^36+1108x^38+1954x^40+2230x^42+3168x^44+2344x^46+2132x^48+1006x^50+788x^52+196x^54+166x^56+10x^58+24x^60+6x^64

The gray image is a code over GF(2) with n=88, k=14 and d=32.
This code was found by Heurico 1.16 in 21.8 seconds.