The generator matrix

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

generates a code of length 44 over Z4 who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+56x^36+84x^37+78x^38+144x^39+161x^40+180x^41+149x^42+164x^43+168x^44+110x^45+127x^46+112x^47+138x^48+90x^49+77x^50+84x^51+43x^52+46x^53+15x^54+8x^55+8x^56+2x^57+2x^58+1x^60

The gray image is a code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.10 in 0.125 seconds.