The generator matrix

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

generates a code of length 56 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 49.

Homogenous weight enumerator: w(x)=1x^0+376x^49+1618x^50+4018x^51+6917x^52+10280x^53+14068x^54+17824x^55+19919x^56+18654x^57+15138x^58+10384x^59+6253x^60+3346x^61+1384x^62+556x^63+220x^64+74x^65+12x^66+14x^67+2x^68+6x^69+2x^70+4x^71+2x^78

The gray image is a code over GF(2) with n=448, k=17 and d=196.
This code was found by Heurico 1.16 in 128 seconds.