The generator matrix

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

generates a code of length 46 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+88x^38+686x^39+2416x^40+6024x^41+10836x^42+19674x^43+29307x^44+39998x^45+42999x^46+41110x^47+29795x^48+19964x^49+10770x^50+5274x^51+1975x^52+802x^53+291x^54+84x^55+26x^56+8x^57+8x^58+4x^59+4x^61

The gray image is a code over GF(2) with n=368, k=18 and d=152.
This code was found by Heurico 1.16 in 360 seconds.