The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+254x^36+398x^38+584x^40+536x^42+569x^44+604x^46+525x^48+336x^50+216x^52+38x^54+26x^56+8x^58+1x^60

The gray image is a code over GF(2) with n=88, k=12 and d=36.
This code was found by Heurico 1.16 in 54.6 seconds.