The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+43x^50+166x^51+154x^52+470x^53+262x^54+774x^55+374x^56+858x^57+293x^58+368x^59+89x^60+134x^61+33x^62+32x^63+16x^64+6x^65+8x^66+2x^67+5x^68+4x^69+1x^70+2x^71+1x^88

The gray image is a code over GF(2) with n=448, k=12 and d=200.
This code was found by Heurico 1.16 in 0.484 seconds.