The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+77x^48+56x^49+164x^50+164x^51+259x^52+340x^53+360x^54+500x^55+353x^56+436x^57+364x^58+300x^59+265x^60+188x^61+110x^62+60x^63+52x^64+4x^65+18x^66+11x^68+2x^70+5x^72+6x^74+1x^76

The gray image is a code over GF(2) with n=224, k=12 and d=96.
This code was found by Heurico 1.16 in 0.804 seconds.