The generator matrix

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

generates a code of length 42 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 35.

Homogenous weight enumerator: w(x)=1x^0+402x^35+1706x^36+4672x^37+9562x^38+18696x^39+31316x^40+41168x^41+46664x^42+41964x^43+30894x^44+19006x^45+9838x^46+4118x^47+1437x^48+492x^49+140x^50+30x^51+20x^52+6x^53+4x^54+6x^55+2x^56

The gray image is a code over GF(2) with n=336, k=18 and d=140.
This code was found by Heurico 1.16 in 442 seconds.