The generator matrix

 1  0  1  1  1  2  1  1  0  0  1  1  1  0  1  1  2  1  1  1  0  1  1 X+2  1  1  1  X X+2  2  1  1  1  0  0  1  1  1  2  X  X  1  1  1
 0  1  1  0  1  1  2 X+1  1  1  2 X+3  2  1  2  1  1 X+3  2  2  1  1  3  1  X  3 X+2  1  1  1  1  1  2  1  1  1  X X+3  1 X+2  1  X  0  2
 0  0  X  0  0  0  0  2 X+2  X X+2 X+2 X+2  2 X+2  X X+2  0  X  2  0 X+2  0 X+2  X  X  X  2 X+2  2  2  X  0  X  2  X X+2  0  2  X  0  0 X+2  2
 0  0  0  X  0  0  2  2  2  2  0  2  2 X+2 X+2  X  X  X  X X+2  X  X X+2  2  2  0  2  X  2  X  X X+2 X+2  X X+2 X+2  0  X  2  2  2  2  X  X
 0  0  0  0  X X+2 X+2  2  X  0  0 X+2  X  X X+2 X+2  X  2  2 X+2  0  2  X X+2  0  X  X X+2  X  0  X X+2  0  2  0  2  0  0  2  2  X  X X+2  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+154x^38+100x^39+418x^40+312x^41+496x^42+348x^43+503x^44+368x^45+516x^46+316x^47+283x^48+88x^49+80x^50+4x^51+64x^52+34x^54+10x^56+1x^60

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 0.569 seconds.