The generator matrix

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

generates a code of length 51 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 43.

Homogenous weight enumerator: w(x)=1x^0+214x^43+983x^44+3286x^45+6088x^46+12794x^47+18557x^48+31410x^49+35414x^50+44536x^51+34736x^52+32262x^53+19556x^54+12490x^55+5450x^56+2768x^57+942x^58+486x^59+109x^60+32x^61+16x^62+8x^63+4x^64+2x^65

The gray image is a code over GF(2) with n=408, k=18 and d=172.
This code was found by Heurico 1.16 in 412 seconds.