The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  X  X  1
 0  X  0 X+2  0 X+2  2 X+2  0 X+2  0  0 X+2 X+2  X  2  2  2  2  0  0
 0  0  2  0  0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  0  0
 0  0  0  2  0  0  0  2  0  0  2  2  2  2  0  0  2  2  0  0  0
 0  0  0  0  2  0  2  0  0  2  0  2  2  0  2  0  2  0  2  2  0
 0  0  0  0  0  2  0  2  2  2  0  2  0  2  0  2  2  2  2  2  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+19x^16+18x^17+29x^18+34x^19+80x^20+156x^21+88x^22+28x^23+18x^24+18x^25+10x^26+2x^27+8x^28+2x^32+1x^34

The gray image is a code over GF(2) with n=84, k=9 and d=32.
This code was found by Heurico 1.16 in 0.00742 seconds.