The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) 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 96 seconds.