The generator matrix

 1  0  0  1  1  1  2 2X  0 2X+2  1  1  1  1  1  1 3X 3X+2  1 3X+2  1  X X+2  1  1  1 3X+2  1  1  1  1  1  1  0 3X+2  1  1  1 3X  0  X  1
 0  1  0  0  3 2X+3  1 3X+2  1  1 3X+2 X+1 3X 3X+3  X 2X  1 2X+2 2X+3  1  3  1  1 3X+1 3X+3 3X X+2  0  1 3X+2  2 2X+2 3X+1  1  1 X+1 X+2 2X+1  1  0 2X+2  0
 0  0  1 X+1 X+1  0 3X+3  1 X+2  1 2X+2  2 2X+3  1 3X+3 3X  3  1  3  X 3X+2 2X+2 3X+3 X+2 X+3 X+1  1  1 2X+1 2X+2  X 2X+2 3X+3 2X+2  3 X+2 X+1 2X+1 2X+3  1  1 2X
 0  0  0 2X+2  2 2X 2X+2  2 2X+2  0 2X+2  2 2X  0  2 2X  2  0  2  2  0 2X  0  2 2X  0 2X  2  0 2X 2X+2 2X 2X+2  2 2X 2X 2X+2 2X+2  0 2X  2 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+192x^37+654x^38+1418x^39+2015x^40+2726x^41+2801x^42+2632x^43+1736x^44+1096x^45+621x^46+334x^47+78x^48+50x^49+25x^50+2x^52+1x^54+2x^58

The gray image is a code over GF(2) with n=336, k=14 and d=148.
This code was found by Heurico 1.16 in 1.64 seconds.