The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+109x^36+274x^37+469x^38+734x^39+944x^40+1338x^41+1623x^42+1732x^43+1924x^44+1878x^45+1590x^46+1262x^47+1003x^48+670x^49+382x^50+226x^51+111x^52+64x^53+29x^54+12x^55+4x^56+3x^58+2x^59

The gray image is a code over GF(2) with n=176, k=14 and d=72.
This code was found by Heurico 1.16 in 7.51 seconds.