The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 48.

Homogenous weight enumerator: w(x)=1x^0+294x^48+1280x^49+3477x^50+6788x^51+12814x^52+19500x^53+30496x^54+35132x^55+41216x^56+36626x^57+31088x^58+19630x^59+12858x^60+6000x^61+2884x^62+1304x^63+487x^64+178x^65+49x^66+26x^67+8x^68+4x^70+2x^72+2x^74

The gray image is a code over GF(2) with n=448, k=18 and d=192.
This code was found by Heurico 1.16 in 470 seconds.