The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  2  1  1  2  1  2  2  1  1  1  2  1  1  2  1  1  1  1  2
 0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  2  2  0  0  2  0  2  2  2  0  2  2  0
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  0  2  2  0  2  0  0  0  0  0  2  2  0  0  2  2  2  0  0  2  2
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  2  2  2  0  2  2  0  0  0  0  2  0  0  0  0  2  2  0  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  2  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  2  0  0  0  2  2  0  0  0  0  0  2  0  2  2  2  2  2  2
 0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  2  0  2  2  0  2  0  0  0  0  0  2  0  2  0  2  2  0  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0
 0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  0  2  0  0  2  0  2  2  2  0  0  0

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

Homogenous weight enumerator: w(x)=1x^0+101x^36+12x^38+191x^40+124x^42+226x^44+100x^46+133x^48+20x^50+85x^52+26x^56+4x^60+1x^72

The gray image is a code over GF(2) with n=88, k=10 and d=36.
This code was found by Heurico 1.16 in 0.171 seconds.