The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+248x^38+392x^39+728x^40+764x^41+780x^42+800x^43+864x^44+828x^45+914x^46+648x^47+495x^48+308x^49+210x^50+80x^51+100x^52+20x^53+6x^54+4x^56+2x^58

The gray image is a code over GF(2) with n=176, k=13 and d=76.
This code was found by Heurico 1.13 in 0.73 seconds.