The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  2  1  0  1  2  1  1  0  1  1  2  1  0  1  0  1  1  1  2  1  2  2  1  1  1  1  1  2  0  2  1  2
 0  1  0  1  0  1  1  0  2  1  3  1  1  0  2  1  1  2  0  1  3  1  1  0  1  1  1  0  2  0  1  3  1  1  3  2  0  0  3  1  1  1  2  0
 0  0  1  1  1  0  1  0  1  3  2  0  1  2  1  1  1  1  3  3  0  0  1  2  0  3  0  0  2  2  1  0  1  1  0  2  0  1  3  3  3  3  1  2
 0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  2  0  2
 0  0  0  0  2  0  0  0  2  0  0  0  0  0  0  0  2  2  2  0  0  0  2  2  2  2  2  0  2  0  2  2  2  0  2  2  0  2  2  0  2  0  2  2
 0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  0  2  0  2  0  2  2  2  2  2  2  0  0  2  0  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  2  2  2  0  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  2  2  2  0  2  2
 0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  0  2  0  0  2  0  0  2  2  2  2  0  0  2  0  0  0  0  2  2  0  2  0  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+91x^36+224x^38+274x^40+329x^42+326x^44+255x^46+215x^48+172x^50+101x^52+40x^54+14x^56+3x^58+2x^60+1x^62

The gray image is a code over GF(2) with n=88, k=11 and d=36.
This code was found by Heurico 1.16 in 0.361 seconds.