The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  2  1  X X^2+X X+2  1 X^2  0  1  1  1  1 X+2  1  0  1 X^2  1  1  1 X^2 X^2+X+2 X^2+X+2  1  1  1  0 X^2+X+2  X  X  1
 0  1  0  0  0  2 X^2+1 X^2+X+3  1 X+1 X^2+X+3  1 X^2+X+2  1 X+2  X  3  1  1 X^2  X X+3 X^2+X+2 X+2  1  1 X^2+X+2 X^2+X+2  2 X+3  3  1 X+2  0  X X^2+X  0 X^2+X X^2+2  1  1 X+3
 0  0  1  0  1 X^2+X+2  2  X X+2 X^2+X+3 X^2+3  3 X^2+X+1 X+1  1  1 X^2+X+3 X+3  1 X+1 X^2 X^2+X+3 X^2+X  1 X^2+X+2 X^2+2  1 X^2+X+2 X^2+2  X X+3 X+2  1  2 X^2+X+1 X^2 X^2+X+1  1  X X+3  X X^2+2
 0  0  0  1  1 X+1 X+3 X+2 X^2+X+3  3 X^2+2 X^2+X X^2+X X^2+3 X^2+3  0  2  3  0 X^2+X+2  1 X^2+X+1 X^2 X+1  X X+2 X^2+1  1 X+1 X^2+X+3 X^2+3 X^2+X+2 X^2+X  1 X^2 X^2+X X^2+1 X+1  1 X+2 X^2  3
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  0  2  0  2  2  0  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+625x^36+2460x^37+5418x^38+9932x^39+15053x^40+20880x^41+21706x^42+21988x^43+15030x^44+9900x^45+5082x^46+1956x^47+749x^48+200x^49+62x^50+12x^51+13x^52+4x^54+1x^56

The gray image is a code over GF(2) with n=336, k=17 and d=144.
This code was found by Heurico 1.16 in 146 seconds.