The generator matrix

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

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+246x^40+128x^42+304x^44+128x^46+199x^48+17x^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 22 seconds.