The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 37.

Homogenous weight enumerator: w(x)=1x^0+98x^37+154x^38+274x^39+494x^40+630x^41+766x^42+686x^43+500x^44+286x^45+98x^46+62x^47+28x^48+10x^49+4x^50+2x^51+2x^58+1x^64

The gray image is a code over GF(2) with n=336, k=12 and d=148.
This code was found by Heurico 1.16 in 101 seconds.