The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+152x^54+176x^55+425x^56+128x^57+95x^58+16x^59+30x^60+1x^106

The gray image is a code over GF(2) with n=448, k=10 and d=216.
This code was found by Heurico 1.16 in 9.95 seconds.