The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X 2X+2
0 2 0 2 0 2 0 2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2 2 2 2X+2 0 0 2X 0 2X 0 2X 2
0 0 2X 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0
0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 2X 2X 2X 0 0 0 2X 0
generates a code of length 28 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 26.
Homogenous weight enumerator: w(x)=1x^0+24x^26+64x^27+76x^28+64x^29+22x^30+3x^32+2x^38
The gray image is a code over GF(2) with n=224, k=8 and d=104.
This code was found by Heurico 1.16 in 0.016 seconds.