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  1  2  1  0  0  1  0  1  1  1  0  0  1  1  1  0  1  1  2  2  1
 0  1  0  0  0  0  0  0  0  0  2  1  3  1  2  3  0  1  1  2  0  2  3  3  1  2  1  1  0  1  1  0  2  2  1  0  2  3  0  2  0  0  1  3
 0  0  1  0  0  0  0  0  0  0  3  2  1  1  0  0  3  3  2  2  2  3  3  0  1  1  3  2  1  1  3  1  1  0  2  3  3  3  1  3  2  2  3  2
 0  0  0  1  0  0  2  1  3  1  1  3  2  1  1  1  1  1  0  2  1  2  0  0  0  3  1  3  0  2  2  2  2  2  0  1  0  2  2  3  2  1  2  0
 0  0  0  0  1  0  3  1  2  3  0  0  0  0  0  2  0  2  3  3  3  2  1  0  1  3  3  3  2  1  2  1  2  1  3  2  3  1  2  0  0  0  1  1
 0  0  0  0  0  1  1  2  3  3  0  0  0  0  2  3  1  0  1  0  3  2  2  3  0  3  1  2  3  0  3  1  2  3  0  2  0  0  1  1  2  2  0  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+384x^38+574x^40+520x^42+670x^44+560x^46+537x^48+264x^50+230x^52+64x^54+32x^56+2x^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 1.52 seconds.