The generator matrix
1 1 1 1 1 1 1 1 1 1 1 X 2 1 X 1 X 1 1 X 1
0 X 0 X 0 0 X X+2 0 2 0 X X X+2 X 0 2 2 0 X+2 X
0 0 X X 0 X+2 X 0 2 X 0 X X+2 2 X+2 2 X 2 0 0 X
0 0 0 2 0 0 0 2 2 2 2 0 2 2 0 2 2 2 2 2 0
0 0 0 0 2 0 0 0 0 0 2 0 2 0 2 2 2 2 0 2 0
0 0 0 0 0 2 0 0 0 2 2 2 0 2 2 0 0 2 0 0 2
0 0 0 0 0 0 2 2 2 2 2 2 0 2 0 0 2 0 0 0 0
generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.
Homogenous weight enumerator: w(x)=1x^0+125x^16+256x^18+642x^20+656x^22+272x^24+48x^26+46x^28+2x^32
The gray image is a code over GF(2) with n=84, k=11 and d=32.
This code was found by Heurico 1.16 in 0.198 seconds.