The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+200x^14+902x^15+2235x^16+4996x^17+9302x^18+15300x^19+20972x^20+23052x^21+21170x^22+15368x^23+9266x^24+5180x^25+2138x^26+684x^27+228x^28+52x^29+22x^30+2x^31+2x^32

The gray image is a code over GF(2) with n=84, k=17 and d=28.
This code was found by Heurico 1.13 in 40.4 seconds.