The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  0  1  1  1 X+2  X  X  X
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  3  1  0  1 X+1 X+2  3  1 X+2  0  0
 0  0  2  0  0  0  0  0  0  2  2  0  2  0  0  2  2  2  2  0  2
 0  0  0  2  0  0  0  2  0  2  2  0  0  2  2  2  0  0  2  2  2
 0  0  0  0  2  0  0  0  2  0  2  0  2  2  2  0  0  2  2  2  0
 0  0  0  0  0  2  0  2  2  0  2  0  2  0  2  2  2  0  0  0  2
 0  0  0  0  0  0  2  2  0  2  0  2  2  2  0  2  2  0  0  2  2

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+78x^16+32x^17+230x^18+128x^19+472x^20+192x^21+470x^22+128x^23+192x^24+32x^25+66x^26+24x^28+2x^30+1x^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 0.0462 seconds.