The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  1 X+2  1  1  0  1  1  1  0  1 X+2  1  1  1  2  1  X  1  1  1  1  X  1  1  0  1  X  2  X  2
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  1  3 X+1  3  0  1 X+1 X+2  1  3 X+3  0  1 X+2  1  3  1  2  1  X  1 X+1  3  1  3 X+2 X+2  1  1  X  X  1  0  X
 0  0  2  0  0  0  0  2  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  0  0  2  2  0  0  0  0  2  0  2  0  2  2  0  2  2  2  2  2  2
 0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  0  2  2  2  0  2  2
 0  0  0  0  2  0  0  2  0  2  2  0  2  0  2  2  2  2  2  2  0  2  2  0  0  2  0  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2
 0  0  0  0  0  2  2  0  0  2  2  0  0  2  0  0  2  2  2  2  2  0  0  2  2  2  0  0  2  0  2  0  2  2  0  0  2  2  0  2  0  0  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+226x^40+160x^42+282x^44+144x^46+177x^48+16x^50+14x^52+3x^56+1x^72

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 0.676 seconds.