The generator matrix

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

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+120x^48+390x^49+588x^50+974x^51+1018x^52+1482x^53+1129x^54+1896x^55+1413x^56+1718x^57+1278x^58+1460x^59+956x^60+804x^61+482x^62+348x^63+131x^64+114x^65+42x^66+22x^67+6x^68+2x^69+1x^70+4x^71+3x^72+2x^73

The gray image is a code over GF(2) with n=224, k=14 and d=96.
This code was found by Heurico 1.16 in 8.9 seconds.