The generator matrix

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

generates a code of length 56 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 47.

Homogenous weight enumerator: w(x)=1x^0+78x^47+442x^48+710x^49+1293x^50+1430x^51+2143x^52+2516x^53+3104x^54+2892x^55+3378x^56+3184x^57+3284x^58+2370x^59+2159x^60+1412x^61+1096x^62+556x^63+400x^64+170x^65+83x^66+32x^67+18x^68+8x^69+4x^70+2x^71+3x^72

The gray image is a code over GF(2) with n=224, k=15 and d=94.
This code was found by Heurico 1.13 in 13 seconds.