The generator matrix

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

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+71x^14+164x^15+389x^16+616x^17+1085x^18+1886x^19+2514x^20+2884x^21+2545x^22+1850x^23+1226x^24+640x^25+283x^26+130x^27+58x^28+20x^29+16x^30+2x^31+4x^32

The gray image is a code over GF(2) with n=84, k=14 and d=28.
This code was found by Heurico 1.16 in 2.65 seconds.