The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+159x^38+88x^39+427x^40+184x^41+688x^42+240x^43+627x^44+240x^45+630x^46+184x^47+341x^48+88x^49+126x^50+37x^52+23x^54+6x^56+6x^58+1x^64

The gray image is a code over GF(2) with n=176, k=12 and d=76.
This code was found by Heurico 1.16 in 2.07 seconds.