The generator matrix

 1  0  0  1  1  1  X  1  1 X+2  1  2  1  1  2 X+2  1  X  1  1  1  1  X X+2  0  1 X+2  1  1  1  1  1  1  2  2  1  1  1  1  0  1 X+2  X  1
 0  1  0  X  1 X+3  1 X+2  0  2  1  1 X+2  3  1  1 X+1  1  3 X+3  2  X X+2  1  1 X+2  1  2  1  0  2 X+1 X+3  1  1  3  1  2  0  1  0  1  1 X+2
 0  0  1  1 X+3 X+2  1 X+1 X+2  1  1  1  0  0  X X+1 X+1 X+2  1  2  1 X+2  1  0 X+1  2 X+3  1  0 X+3  0  3  0  1  2 X+1 X+2 X+2  X  3  2 X+3  3 X+1
 0  0  0  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  2  2  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  2  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  0  0  0  0  2  0  2  0  0  0  2  2  2  2  2  2  2  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  2  2  2  0  2  0  2  2  0  2  2  0  2  0  2  0  2  0  0  2  0  0  2  0  0  0  2  0  2  0  2  2  2  2
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  0  0  2  2  0  2  2  0  0  2  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+76x^37+264x^38+346x^39+629x^40+678x^41+852x^42+654x^43+1078x^44+844x^45+1015x^46+570x^47+532x^48+296x^49+155x^50+90x^51+53x^52+24x^53+13x^54+4x^55+10x^56+2x^57+5x^58+1x^60

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 2.91 seconds.