The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 2 1 X 1 2 X X X X
0 2X+2 0 2 0 0 2 2 2X 2X 2 2X+2 0 2X 2X+2 2X+2 2X 0 2X 2X+2 2 2 2 2 2X 2X 0 2X+2
0 0 2X+2 2 0 2X+2 2X+2 0 2X 2 2 2 0 2 0 2X 2 0 0 2X 2 2X+2 2 2X+2 2 2 2X+2 2X
0 0 0 2X 0 0 2X 0 0 0 0 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 0 2X 2X 0
0 0 0 0 2X 0 0 0 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 0
0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 2X 0 0 0 0 0 2X 2X 2X
generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 24.
Homogenous weight enumerator: w(x)=1x^0+200x^24+184x^26+256x^27+786x^28+256x^29+192x^30+141x^32+8x^34+22x^36+2x^40
The gray image is a code over GF(2) with n=224, k=11 and d=96.
This code was found by Heurico 1.16 in 0.765 seconds.