The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  1  X  1  X  1  1  1  1  1  1  X  X  1  X  1  X
 0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  0  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  0  0  0  2  2  0  0  2  2  2  0  2  0  0  0  2  2  2  0  0  0  2  0
 0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  0  2  0  2  2  2  2  2  2  0  0  2  2  0  0  0  2  2  2  0  2  0  0  0  0  0  2
 0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  0  0  0  0  2  2  2  0  2  0  0  2  2  2  2  2  0  0  0  0  0  2
 0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  0  0  2  2  0  0  2  2  2  0  2  0  2  0  2  2  0  0  2  2  0  2  0
 0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  2  2  0  2  2  0  2  2  0  2  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  0  2  2  2  2  2  0  2  2  2  0  0  0  0  2  2  0  0  2  0  0  2  2  0  0  0  0
 0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  2  2

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+109x^36+16x^38+170x^40+112x^42+1259x^44+112x^46+151x^48+16x^50+67x^52+29x^56+5x^60+1x^72

The gray image is a code over GF(2) with n=176, k=11 and d=72.
This code was found by Heurico 1.16 in 2.56 seconds.