The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  2  2  2  1  0  1  1  1  2  0  0  1  2  1  2  1  0  1  1  1  0  1  1  1  2  1  1  0  1  2  1  1
 0  1  0  0  0  1  1  1  0  0  1  3  1  0  1  2  1  2  0  1  1  2  1  0  0  1  1  1  0  1  1  1  1  2  1  1  0  2  2  0  2  1  0  2
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  3  2  1  1  0  3  0  1  2  1  1  0  3  2  0  1  1  2  3  1  2  0  2  3  0  1  0  0  0  1
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  2  3  3  0  0  2  3  0  0  1  1  3  0  0  1  3  2  2  3  0  1  0  1  3  3  3  1  0  3  2
 0  0  0  0  2  0  0  0  0  0  0  0  2  2  0  0  0  2  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  0  2  2  2  2  0  2  0  0  2  2  2  0  2  0  2  2  0  0  2  2  0  2  2
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  2  0  2  2  2  0  2  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  0
 0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  0  0  2  2  2  0  2  0  0  2  2  0  2  2  2
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  2  2  2  2  2  2  0  2
 0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  2  0  2  0  2  2  0  0  0  0  2  0  2  0  0  0  2  0  2  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+286x^32+576x^34+1505x^36+2298x^38+3954x^40+4774x^42+5651x^44+5060x^46+4278x^48+2188x^50+1441x^52+418x^54+246x^56+46x^58+41x^60+3x^64+2x^68

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 75 seconds.