The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  2  1  1  2  2  1  0  1  0  1  1  2  1  1  1  1  1  0  1  0  2  0  1  1  1  1  2  0  2  1  1
 0  1  0  1  0  1  1  0  0  1  3  1  1  2  0  1  1  1  2  1  3  0  0  3  1  1  0  2  3  2  2  0  2  1  1  1  1  2  0  1  2  0  0  0
 0  0  1  1  1  0  1  0  1  1  0  2  1  1  0  3  1  3  1  0  0  1  2  3  2  1  2  1  0  1  1  0  1  1  3  3  2  0  0  3  1  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  2  0  0  2  2  2  0  0  0  2  2  2  2  0  0  2  2  0  0  2  0  0  0
 0  0  0  0  2  0  0  0  0  0  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0  2  2  0  0  0  2  0  2  2  0  2  2  2  2  0  2  0  0
 0  0  0  0  0  2  0  0  0  0  2  0  2  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  0  2  0  2  0  2  0  2  0  2  2  0  0  0  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  0  2  2  0  2  2  2  2  0
 0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  2  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  2  2  0  0  0  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  0  2  2  2  0  2  0  0  0  2  0  2  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+45x^32+185x^34+398x^36+662x^38+932x^40+1178x^42+1327x^44+1273x^46+992x^48+613x^50+332x^52+160x^54+61x^56+24x^58+7x^60+1x^62+1x^72

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 5.45 seconds.