The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X 2X+2  X  0  X  X  X  2
 0  X 2X+2 X+2  0 X+2 2X+2 3X  0 X+2 2X+2 3X  0 X+2 2X+2  X 2X 3X+2  2  X 2X 3X+2  2 3X 2X 3X+2  2  X 2X 3X+2  2 3X X+2  X 3X  X X+2  X X+2 3X+2  0  0
 0  0 2X  0  0 2X 2X 2X 2X  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0  0 2X 2X  0  0
 0  0  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0 2X 2X  0  0  0  0 2X 2X  0 2X 2X  0 2X  0  0 2X  0  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+124x^40+64x^41+104x^42+128x^43+80x^44+8x^46+2x^48+1x^64

The gray image is a code over GF(2) with n=336, k=9 and d=160.
This code was found by Heurico 1.16 in 0.047 seconds.