The generator matrix

 1  0  0  1  1  1  X  1 X+2  1  1  X  1  2  1  1  1  2  1 X+2  X  1 X+2  1  X  1  1  1  1  1  2  1  1  2  1  1 X+2  1  1  1  1  1  X  1
 0  1  0  0  1 X+3  1  2  0  2 X+3  1 X+1  1  1  2  X  1  1  X  1  0  1  1  1 X+1 X+2  2  0 X+1  1 X+2 X+2  1  2  1  1 X+1 X+2 X+2  3 X+1  1  0
 0  0  1  1 X+1  0  1 X+1  1  X X+1  X  0 X+1 X+1 X+3  0  X  2  1 X+3  2 X+1 X+1  X  X  3 X+2  1 X+1  3  0 X+1  2  1  0 X+3 X+3  3 X+2  X X+2  0  0
 0  0  0  X  X X+2  2 X+2  0  0  X  2  0 X+2  2  2 X+2  X  2  X  X X+2  0  0 X+2  X X+2  X  2  2  2 X+2  X  X  2  X  2  0  0  0  0  2  X  2
 0  0  0  0  2  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  0  0  2  0  2  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0  0  2
 0  0  0  0  0  2  2  0  0  0  0  0  2  2  0  0  0  0  2  0  2  0  2  0  2  0  2  2  2  2  0  2  2  0  2  2  0  2  2  0  0  2  0  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+94x^37+178x^38+490x^39+417x^40+882x^41+641x^42+1108x^43+660x^44+1150x^45+619x^46+832x^47+363x^48+406x^49+132x^50+124x^51+28x^52+28x^53+26x^54+6x^55+3x^56+3x^58+1x^62

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 2.07 seconds.