The generator matrix

 1  0  1  1  1  X  1  1  2  1  1  0  1  1 X+2  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  1  2  1  X  0  1  1  1  1  1  1  1  1  1
 0  1  1  2 X+1  1  X  3  1  0  1  1 X+2 X+3  1 X+2 X+3  1  0 X+3  1 X+2  1  1  2  X  2  X  2  X X+1  1  3  1  0  0 X+2 X+1  3 X+3  3  1 X+1  0
 0  0  X X+2  2 X+2  X  0  X  2 X+2  2  0  X  0  2 X+2  2 X+2  2  X  X  0 X+2  2  2  0  0  X X+2  0 X+2  2  X  X  X X+2 X+2 X+2  0  X  2  X  0

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+27x^42+64x^43+77x^44+64x^45+11x^46+9x^48+1x^52+1x^54+1x^66

The gray image is a code over GF(2) with n=176, k=8 and d=84.
This code was found by Heurico 1.16 in 0.028 seconds.