The generator matrix

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

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+32x^36+92x^37+134x^38+268x^39+143x^40+480x^41+147x^42+698x^43+151x^44+746x^45+134x^46+478x^47+126x^48+174x^49+71x^50+86x^51+53x^52+42x^53+23x^54+6x^55+6x^56+2x^57+2x^58+1x^62

The gray image is a code over GF(2) with n=176, k=12 and d=72.
This code was found by Heurico 1.16 in 0.737 seconds.