The generator matrix

 1  0  1  1  1 X+2  1  1 X+2  1  1  0  1  1  2  1  1  X  1  1  1  1  2  X  X  X  0  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2  X X+3  1  1  1  0 X+2  X  0  2 X+1 X+3 X+2 X+2  3  3  0  2  X  X X+1 X+3  1  1  0
 0  0  2  2  0  2  2  0  0  0  2  2  2  2  2  0  0  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  2  0  2  0  2  0  2  0  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+6x^42+48x^43+12x^44+48x^45+8x^46+3x^48+1x^50+1x^66

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 0.026 seconds.