The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+78x^40+130x^41+205x^42+98x^43+168x^44+72x^45+79x^46+36x^47+57x^48+18x^49+19x^50+26x^51+32x^52+4x^53+1x^54

The gray image is a code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.16 in 0.0546 seconds.