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

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+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 41.6 seconds.