The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+28x^42+16x^43+167x^44+16x^45+20x^46+5x^48+1x^52+2x^60

The gray image is a code over GF(2) with n=352, k=8 and d=168.
This code was found by Heurico 1.16 in 0.047 seconds.