The generator matrix

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

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+49x^38+228x^39+334x^40+442x^41+418x^42+458x^43+433x^44+476x^45+307x^46+320x^47+230x^48+170x^49+112x^50+50x^51+31x^52+32x^53+2x^54+3x^56

The gray image is a code over GF(2) with n=176, k=12 and d=76.
This code was found by an older version of Heurico in 0 seconds.