The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  X  1  2  2  1  1  1  X  1  1 X+2  1  X  1  2  1  0  1  1  1  X  1 X+2  0  1  2  1  1  0  2  X  1  1
 0  1  1 X+2 X+3  1  0 X+1  1  X  3  1  0  1  1  1  2 X+1  1 X+3 X+2  1  3  1  2  1 X+3  1  X  2  X  1  3  1  1 X+1  1  3  0  X  1  X X+2  0
 0  0  X  0 X+2  0 X+2  0 X+2 X+2  2  X  2  X  0  X X+2  2  X  X  0  0  0  2 X+2 X+2 X+2 X+2 X+2 X+2 X+2  X  2  2  2  2  2  2  0 X+2 X+2 X+2  2  0
 0  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  2  2  2  0  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  2  0  2  2  2  2
 0  0  0  0  2  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  2  2  2  2  2  0  0  2  0  0  2  0  0  0  2  0  2  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  2  0  2  2  2  2  2  0  0  2  2  2  0  2  0  0  0
 0  0  0  0  0  0  2  0  2  2  0  0  0  2  0  0  2  0  0  0  2  2  2  2  0  2  0  0  2  2  0  2  0  0  2  2  0  0  0  0  2  2  0  2
 0  0  0  0  0  0  0  2  2  0  2  0  0  2  0  0  0  2  0  0  0  2  2  2  0  0  2  2  2  0  2  2  0  2  2  0  0  0  2  2  0  2  0  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+95x^36+40x^37+330x^38+104x^39+814x^40+344x^41+1160x^42+536x^43+1421x^44+536x^45+1164x^46+344x^47+721x^48+104x^49+264x^50+40x^51+121x^52+26x^54+24x^56+3x^60

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 2.33 seconds.