The generator matrix

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

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+50x^37+81x^38+136x^39+83x^40+402x^41+575x^42+392x^43+86x^44+118x^45+47x^46+40x^47+20x^48+6x^49+1x^50+8x^51+1x^52+1x^76

The gray image is a code over GF(2) with n=336, k=11 and d=148.
This code was found by Heurico 1.16 in 41.1 seconds.