The generator matrix

 1  0  0  1  1  1  0  1  2  1  1  2  1  2 X+2  1  1  X  X  1 X+2  X  1  1  1 X+2  1  1  1  1 X+2 X+2  1  1  2  1 X+2  1  2  1  X  X  X  1
 0  1  0  0  1  3  1  X  1  1  2  1 X+1 X+2  1 X+2 X+3  1  X  X  1  1  2 X+1  3  0  X  1  2  X  1  1 X+3 X+1  X  1 X+2  2  X  X  1  1 X+2 X+3
 0  0  1 X+1 X+3  0 X+1  1  X  1  X  3  0  1  X  2  X X+3  1 X+3  2  3  3 X+3 X+2  1 X+2 X+1 X+1  3  2 X+2  0 X+1  1  1  1 X+3  1 X+3  1  1  1 X+2
 0  0  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  2  0  0  0  2  0  2  2  0  0  0  0  0  0  0  2  2  2  2  0  0
 0  0  0  0  2  2  2  0  2  2  0  2  2  0  2  0  2  2  2  2  0  0  2  0  0  2  2  2  2  0  2  2  0  0  2  0  2  0  2  0  0  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+352x^40+528x^42+518x^44+284x^46+223x^48+72x^50+50x^52+12x^54+8x^56

The gray image is a code over GF(2) with n=176, k=11 and d=80.
This code was found by Heurico 1.16 in 1.06 seconds.