The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+283x^38+840x^39+1141x^40+1428x^41+1256x^42+1160x^43+932x^44+620x^45+296x^46+156x^47+40x^48+16x^49+12x^50+4x^51+6x^52+1x^54

The gray image is a code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 0.422 seconds.