The generator matrix

 1  0  1  1  1 X+2  1  1  2  X  1  1  2  1  1  1  X  1  X  1  1  1 X+2  1 X+2  2  2  2  1  1  1  1  X  X  1  X X+2  1  1  1  1  1  2  1
 0  1  1 X+2 X+3  1  2 X+1  1  1  X  3  1  1  0 X+3  1  2  1 X+1  2 X+2  1 X+3  1  1  1  1 X+3  3 X+2 X+3  1  1  0  1  1  3  1  3  0  0  X  0
 0  0  X  0 X+2  0  X  2 X+2 X+2  X  2  X  X  0  X  2 X+2 X+2  2  2  0  0  X  0  X  0 X+2  0  2  0  2  X  0  0 X+2  X  2  0  2 X+2  X X+2  0
 0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  2  0  2  2  0  2  2  2  2  0  0  2  2  0  0  2  0  0  0  0  0  2  2  0  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  0  0  0  2  0
 0  0  0  0  0  2  2  0  2  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  2  0  2  2  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+31x^38+144x^39+80x^40+320x^41+101x^42+302x^43+117x^44+352x^45+100x^46+270x^47+37x^48+120x^49+14x^50+18x^51+12x^52+8x^53+9x^54+2x^55+6x^56+1x^58+3x^60

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.165 seconds.