The generator matrix

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

generates a code of length 47 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 39.

Homogenous weight enumerator: w(x)=1x^0+62x^39+638x^40+2330x^41+5674x^42+11070x^43+19271x^44+29686x^45+40118x^46+43170x^47+40818x^48+30906x^49+19798x^50+10692x^51+5003x^52+1814x^53+706x^54+278x^55+59x^56+28x^57+8x^58+6x^59+2x^60+4x^61+2x^63

The gray image is a code over GF(2) with n=376, k=18 and d=156.
This code was found by Heurico 1.16 in 373 seconds.