The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+154x^36+1332x^37+2760x^38+5036x^39+7593x^40+10296x^41+11154x^42+10584x^43+7456x^44+5126x^45+2554x^46+1028x^47+284x^48+124x^49+43x^50+8x^51+2x^53+1x^58

The gray image is a code over GF(2) with n=336, k=16 and d=144.
This code was found by Heurico 1.16 in 19.8 seconds.