The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X 2 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 2X 2X 0 0 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 2X 2X 0 0 0 0 0
generates a code of length 28 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 20.
Homogenous weight enumerator: w(x)=1x^0+29x^20+66x^24+128x^26+256x^27+1094x^28+256x^29+128x^30+60x^32+25x^36+4x^44+1x^48
The gray image is a code over GF(2) with n=224, k=11 and d=80.
This code was found by Heurico 1.16 in 0.046 seconds.