The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  1  X X+2  X  X  2  0  1  1  1  1  1  1  2  1  1  1  1 X+2  1  2  1  1  2  0  1  0  1  2  1  1  1  2
 0  1  0  X  1 X+3  1 X+2  0  2  1 X+1  1  1  X  1  X  1  X  3  2 X+3 X+2  1  1  0  X X+1  3  1  2  1 X+2 X+2 X+2  1 X+1  1 X+1  1  0  3  0  X
 0  0  1  1 X+3 X+2  1 X+3 X+2  1  1  0  X X+1  1  2  1 X+1  X  0  1  3  0 X+2  1 X+1  1  2  3 X+3  3 X+3 X+2  2  1  X  1  2  1 X+1  1  2 X+1  0
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  2  0  0  0  2  0  2  0  2  0  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  0  2  2  2  2  0  0  0  2  2  2  0  0  2  2  0  2  0  0  0  2  2  2  2
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  0  2  2  2  2  0  0  2  0  0  0  2  0  2  2  2  0  2  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  0  0  2  0  0  0  2  2  2  0  0  2  2  2  0  2  0  2  2  2  2  0  0  2  2  0  0  2  2  2  2  0  2
 0  0  0  0  0  0  0  2  2  2  2  2  0  0  2  0  0  0  2  0  2  0  2  0  2  2  2  0  2  2  0  2  2  2  2  0  0  0  0  2  0  0  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+151x^36+204x^37+484x^38+608x^39+1058x^40+1328x^41+1490x^42+1936x^43+1846x^44+1944x^45+1600x^46+1408x^47+957x^48+592x^49+348x^50+144x^51+191x^52+28x^53+44x^54+16x^56+2x^58+4x^60

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 7.04 seconds.