The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  X  2  X
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  2  X  2  X  2  X  2  X X+3  1 X+3  1 X+3  1 X+3  1  1  1  0  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  2  0
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  2  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+56x^42+32x^43+82x^44+32x^45+40x^46+10x^48+2x^52+1x^64

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 0.0284 seconds.