The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+829x^36+2248x^37+5404x^38+9644x^39+15632x^40+19320x^41+24288x^42+20332x^43+15966x^44+9208x^45+5082x^46+2020x^47+779x^48+200x^49+100x^50+4x^51+9x^52+6x^54

The gray image is a code over GF(2) with n=336, k=17 and d=144.
This code was found by Heurico 1.16 in 359 seconds.