The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 40.

Homogenous weight enumerator: w(x)=1x^0+18x^40+90x^41+57x^42+60x^43+12x^44+10x^45+6x^46+1x^52+1x^62

The gray image is a code over GF(2) with n=336, k=8 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.