The generator matrix

 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  X  1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  1  1  1  1  1  1  1
 0  2  0  0  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  0  2  0  0  0  2  0  2  0  2  2  0  2  2  0  2  2  2  0  2  0  0  0  2  0  2  0
 0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  0  0  0  0  0  2  2  2  2  2  0  0  2  2  2  0  2  0  2  0  0  2  2  0  2  0  0  2  0  0  0  2  0  0  2  0  2  0  2  0  0
 0  0  0  2  0  0  0  0  2  0  0  2  0  2  2  2  0  0  2  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  0  2  2  0  0  0  0  2  0  0  2  0  0  2  2  0  0  0  2  0  0  0
 0  0  0  0  2  0  0  0  2  0  2  2  0  2  0  2  2  2  0  0  0  0  0  0  2  2  0  2  0  2  2  0  2  2  0  2  0  0  0  2  2  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2
 0  0  0  0  0  2  0  0  2  0  2  0  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  2  0  0  0  2  0  2  2  0  2  0  0  2  0  2  2  2  0  0  2  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  2  0  2  2  0  0  2  2  0  2  0  2  2  0  0  0  2  2  2  2  0  0  0  2  0  2  0  0  0  0  0  0  2  0  2  2  2  2  2  0  0  2  2  0  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  2  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2  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+42x^48+97x^52+64x^54+639x^56+64x^58+66x^60+35x^64+13x^68+2x^72+1x^104

The gray image is a code over GF(2) with n=224, k=10 and d=96.
This code was found by Heurico 1.16 in 0.155 seconds.