The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  1 X+2  X  1  1  1  X  1  1  X  1  X  0 X+2  1  1  1  1  1  1  1  2 X+2  2  0  1  1  0  2  1
 0  1  0  0  1 X+1  1 X+2  3  1  X  3 X+2  1 X+3  1  1  1 X+2  0  X X+3  0  1 X+1 X+2  2  1  0 X+2  3  1 X+2  0  2  X  1  1  1 X+2 X+3  1  1  2
 0  0  1  1  1  0  1  3  1  1  1  0  2  X  1  X  1  2 X+1  2  1 X+1  X X+2  2  1  1 X+3 X+2 X+1  1 X+1 X+3 X+3  1  1  1  0 X+3  2  2  X  0  0
 0  0  0  X  0  0  2  2 X+2  X  X X+2  X X+2 X+2  X  2  X  X X+2 X+2  2  2  0  2  2  0 X+2  2  2  0 X+2  0  2 X+2  2  2  X  2  X X+2  0  2  2
 0  0  0  0  X  2  X X+2  2  2 X+2  X  X X+2 X+2  0  2  2 X+2  2  2  0  X X+2 X+2  0 X+2 X+2  0  2  2  2  2 X+2  0  0 X+2 X+2  0 X+2  0  0  X X+2

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+70x^37+242x^38+386x^39+581x^40+686x^41+817x^42+928x^43+887x^44+912x^45+845x^46+678x^47+414x^48+326x^49+223x^50+84x^51+61x^52+22x^53+13x^54+4x^55+8x^56+4x^58

The gray image is a code over GF(2) with n=176, k=13 and d=74.
This code was found by Heurico 1.16 in 2.11 seconds.