The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+162x^32+144x^33+397x^34+532x^35+770x^36+884x^37+1246x^38+1600x^39+1879x^40+2050x^41+2332x^42+2946x^43+2557x^44+2708x^45+2581x^46+2568x^47+2018x^48+1500x^49+1285x^50+912x^51+660x^52+356x^53+296x^54+136x^55+131x^56+34x^57+50x^58+10x^59+13x^60+4x^61+5x^62+1x^64

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 72.6 seconds.