The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+258x^36+400x^38+549x^40+548x^42+635x^44+584x^46+453x^48+388x^50+186x^52+64x^54+29x^56+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 1.10 in 3.41 seconds.