The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+336x^51+940x^52+1766x^53+1922x^54+2386x^55+2366x^56+2250x^57+1661x^58+1208x^59+663x^60+498x^61+192x^62+100x^63+52x^64+30x^65+9x^66+1x^68+2x^71+1x^72

The gray image is a code over GF(2) with n=448, k=14 and d=204.
This code was found by Heurico 1.16 in 2.19 seconds.