The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+72x^39+264x^40+232x^41+96x^42+208x^43+363x^44+208x^45+96x^46+232x^47+152x^48+72x^49+36x^52+14x^56+1x^60+1x^64

The gray image is a code over GF(2) with n=176, k=11 and d=78.
This code was found by Heurico 1.16 in 0.265 seconds.