The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  0  1  1  X  2  X  1  0  0  1  X  X  0  X  1  1  1  1
 0  X  0  X  0  0  X X+2  0  2 X+2  X  0  X  X  2  2 X+2  0  X X+2  0  0  X  0 X+2  X  2  X  X  X X+2 X+2  0  0  2 X+2  0  2 X+2  X  X  X X+2
 0  0  X  X  0 X+2  X  0  2  X  0  X  0 X+2  2  X  X  2  0 X+2 X+2 X+2  X  2  X  0  2  0  2  X  X  0  X  X  X  0  X X+2  X  0  0 X+2  X  0
 0  0  0  2  0  0  0  0  2  2  2  2  2  0  2  0  0  0  0  2  0  0  2  0  2  2  0  2  0  2  2  2  2  0  0  2  2  0  2  2  2  0  2  2
 0  0  0  0  2  0  0  0  0  0  0  2  2  2  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  2  2  0  0  2  0  2  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  0  2  0  0  0  0  0  2  0  0  0  2  0  0  2  0  2  0  2  0  2  2  2
 0  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  0  2  2  2  2
 0  0  0  0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  0  0  2  2  0  0  0  0  2  2  2  0  2  0  0  2  2  2  0  0  0  0  2  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+68x^36+76x^37+126x^38+184x^39+236x^40+342x^41+398x^42+426x^43+433x^44+494x^45+366x^46+234x^47+233x^48+210x^49+108x^50+46x^51+42x^52+30x^53+18x^54+6x^55+10x^56+6x^58+1x^60+2x^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 0.778 seconds.