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  1  1  1  1  1  X  1  1  0  X  1  X  1  1  1  1  1  X  1  2
 0  X  0  X  0  0  X X+2  0  2  X X+2  0 X+2  2 X+2  2  2  X  X X+2  2  2  X X+2  0  0  0 X+2 X+2  X  X  X  0  0  X X+2  0  2 X+2 X+2 X+2 X+2  0
 0  0  X  X  0 X+2  X  0  2  X  X  0  2 X+2  X  0 X+2  2  X  2  X  0 X+2  0  0  2  0  X X+2  0  2 X+2  2 X+2  0 X+2  2  X X+2  X  X  2  X  0
 0  0  0  2  0  0  0  2  2  2  0  0  2  2  0  2  2  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  0  0  0  2  2  0  0  2  0
 0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  0  2  2  0  2  2  2  0  2  0  0  0  0  2  2  0  2  0  0  2  2  2  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  2  2  2  2  0  0  2  2  2  0  0  2  0  2  0  0  0  0  2  0  2  0  0  2  0  0  0  0  2  0  2  2  2  2  2
 0  0  0  0  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  2  2  2  0  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  2  2  0  2  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+170x^38+178x^40+434x^42+541x^44+403x^46+139x^48+126x^50+34x^52+18x^54+2x^56+1x^62+1x^76

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 4.51 seconds.