The generator matrix

 1  1  1  1  1  1  1  1  1  X  X  1  X  X  X  1  X  1  X  1  1
 0  X  0  0  0  X X+2  X  0  0  2  2 X+2 X+2  X  2 X+2  2  0 X+2 X+2
 0  0  X  0  X  X X+2  0  0  X  2  X  X  X  X  X  0  2 X+2  X  0
 0  0  0  X  X  0 X+2  X  2  X X+2  0  X X+2  0 X+2  2  X  2  2  0
 0  0  0  0  2  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0
 0  0  0  0  0  0  2  0  2  2  2  0  0  2  2  0  0  0  2  2  2
 0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  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+100x^14+409x^16+96x^17+931x^18+384x^19+1630x^20+1088x^21+1598x^22+384x^23+1044x^24+96x^25+300x^26+114x^28+14x^30+2x^32+1x^34

The gray image is a code over GF(2) with n=84, k=13 and d=28.
This code was found by Heurico 1.16 in 0.824 seconds.