The generator matrix

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

generates a code of length 42 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+103x^36+682x^37+1474x^38+2602x^39+3741x^40+5312x^41+5293x^42+5172x^43+3589x^44+2546x^45+1264x^46+644x^47+218x^48+52x^49+57x^50+12x^51+4x^52+2x^55

The gray image is a code over GF(2) with n=336, k=15 and d=144.
This code was found by Heurico 1.16 in 6.16 seconds.