The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 36.

Homogenous weight enumerator: w(x)=1x^0+184x^36+1218x^37+2987x^38+4888x^39+7691x^40+9936x^41+11354x^42+10456x^43+8044x^44+4762x^45+2526x^46+982x^47+326x^48+128x^49+34x^50+8x^51+2x^52+4x^53+3x^54+2x^55

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 19.4 seconds.