The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  1  1 X+2  X  1  1  1  2  1 X+2  1  1  1  1  1  1  1  1  1  1  0  1  1  X  1  1  1  1  1  1  1  1
 0  1  1 X+2 X+1  1  3  2  1  2  1  1  X X+3  1  1  2 X+3 X+2  1 X+2  1  1 X+3 X+3  1 X+1  3 X+1  3 X+1  3  0  0  X  2  2  X  0  0  X X+2  X  0
 0  0  X  0  2  0  2  X  X X+2 X+2 X+2  X  X  0  X  0  2 X+2  0  0 X+2  2  X X+2 X+2  0  2 X+2  X  2  0  X  2  0  2 X+2 X+2  X  0  2  2 X+2  0
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  2  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 41.

Homogenous weight enumerator: w(x)=1x^0+76x^41+110x^42+80x^43+46x^44+48x^45+80x^46+24x^47+15x^48+16x^49+2x^50+8x^51+1x^52+4x^57+1x^68

The gray image is a code over GF(2) with n=176, k=9 and d=82.
This code was found by Heurico 1.16 in 0.0439 seconds.