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

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+230x^36+468x^38+16x^39+705x^40+280x^41+996x^42+704x^43+1336x^44+784x^45+1086x^46+240x^47+681x^48+24x^49+382x^50+170x^52+70x^54+12x^56+6x^58+1x^72

The gray image is a code over GF(2) with n=176, k=13 and d=72.
This code was found by Heurico 1.16 in 29.2 seconds.