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

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+40x^36+30x^37+68x^38+62x^39+127x^40+134x^41+179x^42+294x^43+218x^44+282x^45+180x^46+122x^47+101x^48+66x^49+61x^50+34x^51+22x^52+14x^54+3x^56+7x^58+2x^62+1x^66

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 0.246 seconds.