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.