The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+250x^17+413x^18+404x^19+701x^20+596x^21+678x^22+472x^23+323x^24+162x^25+53x^26+36x^27+7x^28

The gray image is a code over GF(2) with n=84, k=12 and d=34.
This code was found by Heurico 1.11 in 519 seconds.