The generator matrix

 1  0  0  1  1  1  2  0  1  1  0  2  1  1  X  X  1  2  1  1  1  0  X  1  1  1 X+2  1  1  X  1  2 X+2  1  1  1  1  1  1  1  1  1  1  1
 0  1  0  0  1  1  1  X  2  3  1  1  2  3  0 X+2  1  1  2  X  1  1  2  2 X+2 X+1  1 X+2 X+3  1  1  1  1 X+3  X X+1  3 X+3 X+3 X+1  1  3  1  0
 0  0  1  1  2  3  1  1  X X+2  X X+3 X+1 X+3  1  1  X  1  3 X+2 X+1  2  1  2  1 X+2  3  0  0 X+3  1  X X+2 X+1 X+1  0  0 X+1  1  1  X  3 X+2  0
 0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  0  0  2  0  2  2  0  2  2  2  2  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+55x^40+228x^41+41x^42+232x^43+82x^44+148x^45+28x^46+64x^47+27x^48+60x^49+6x^50+24x^51+10x^52+12x^53+4x^54+1x^56+1x^58

The gray image is a code over GF(2) with n=176, k=10 and d=80.
This code was found by Heurico 1.11 in 0.0383 seconds.