The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+242x^38+760x^39+1429x^40+1230x^41+1377x^42+1078x^43+918x^44+574x^45+354x^46+114x^47+80x^48+20x^49+10x^50+4x^52+1x^58

The gray image is a code over GF(2) with n=336, k=13 and d=152.
This code was found by Heurico 1.16 in 0.406 seconds.