The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+45x^36+92x^37+113x^38+130x^39+147x^40+158x^41+159x^42+166x^43+141x^44+122x^45+134x^46+146x^47+130x^48+102x^49+73x^50+66x^51+42x^52+34x^53+28x^54+4x^55+6x^56+4x^57+4x^58+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 0.335 seconds.