The generator matrix

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

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 42.

Homogenous weight enumerator: w(x)=1x^0+26x^42+16x^43+44x^44+16x^45+16x^46+1x^48+4x^50+2x^52+2x^54

The gray image is a code over GF(2) with n=176, k=7 and d=84.
This code was found by Heurico 1.16 in 0.0264 seconds.