The generator matrix

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

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+78x^41+80x^42+104x^43+71x^44+46x^45+57x^46+28x^47+7x^48+12x^49+5x^50+16x^51+4x^53+2x^54+1x^56

The gray image is a code over GF(2) with n=176, k=9 and d=82.
This code was found by Heurico 1.13 in 0.015 seconds.