The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+189x^36+1134x^37+2822x^38+5360x^39+7427x^40+10510x^41+10503x^42+10688x^43+8083x^44+4946x^45+2244x^46+1144x^47+308x^48+114x^49+37x^50+24x^51+2x^58

The gray image is a code over GF(2) with n=336, k=16 and d=144.
This code was found by Heurico 1.16 in 22.1 seconds.