The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  0  X  1  1  1  1  X  X  X  0  0  0  X  1  1  1  1  1  1  1  2  2
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  2 X+2  2  X  2 X+2  X  2  2  X  2 X+2 X+2 X+2  0  X  X  X  X  2  X  2  X  2 X+2  2  0  2
 0  0  2  0  0  0  2  0  0  2  0  2  2  2  2  2  2  0  2  0  0  0  0  2  2  0  2  0  0  0  2  0  2  2  0  0  2  0  2  0  2  0  2  2
 0  0  0  2  0  0  0  2  2  2  2  2  2  0  2  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  2  2  2  0  0  2  0  0  2  2  2  0  2  0
 0  0  0  0  2  2  2  2  2  0  0  2  0  2  2  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  2  2  0  2  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+28x^41+90x^42+22x^44+24x^45+63x^46+7x^48+12x^49+6x^50+2x^52+1x^62

The gray image is a code over GF(2) with n=176, k=8 and d=82.
This code was found by Heurico 1.16 in 17.9 seconds.