The generator matrix

 1  0  1  1  1  0  1  1  0  1  2  1  1  1 X+2  1  X  1  1  X  X  1  1  1 X+2 X+2  1  X  1  1  1 X+2 X+2  X  1  1  1  1  0  2 X+2  1  0  1
 0  1  1  0  1  1  2 X+1  1  0  1  3 X+3  0  1  1  1  2  2  1  1  3 X+2  1  1  1 X+2  1 X+2  2 X+1  1  1 X+2 X+1  2  3  0  2  1  1 X+1  1  2
 0  0  X  0  0  0  0  0  0  0  0  0  2  X X+2 X+2 X+2 X+2 X+2  X  X  X  X X+2  2  2  2  X  2 X+2  0  2  0 X+2 X+2  2  X  X  X X+2  X  2 X+2  0
 0  0  0  X  0  0  0  0  X X+2 X+2  X X+2 X+2 X+2 X+2  0 X+2  2 X+2  2  0  2  X  X  2  0  X  X  2  2 X+2  0  X  X X+2  0  2  0 X+2  0  0  2  0
 0  0  0  0  X  0  2 X+2  0  2  0 X+2  X  X  X  2  X X+2  X  X  X  2 X+2  0  0  2  2  0 X+2  0  2 X+2  X  0 X+2 X+2 X+2  0  2 X+2  X  X X+2  0
 0  0  0  0  0  X X+2 X+2 X+2 X+2  2  2  X X+2 X+2  2  2  0 X+2  0  X X+2  0 X+2  X X+2  2 X+2  2  0  0  X  2  X  X  2  2  X  0  0  0 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+265x^36+92x^37+628x^38+392x^39+1198x^40+976x^41+1880x^42+1576x^43+2349x^44+1680x^45+1900x^46+952x^47+1173x^48+384x^49+512x^50+88x^51+240x^52+4x^53+72x^54+20x^56+1x^60+1x^68

The gray image is a code over GF(2) with n=176, k=14 and d=72.
This code was found by Heurico 1.16 in 19.7 seconds.