The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  2  X  X  X  1
 0  X  0  0  0  0  0  0  0 X+2  X  X  X  2  2  X  0  2 X+2  X  0
 0  0  X  0  0  0  X X+2  X  2  X X+2  0  2  0  0  X  2  X  2  0
 0  0  0  X  0  X  X  X  0 X+2  2  2 X+2  X  X X+2  2  0 X+2  2  0
 0  0  0  0  X  X  0  X X+2  X  0  2  2 X+2  2  X X+2 X+2  0  X  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  0  2  0  2
 0  0  0  0  0  0  2  0  2  0  2  2  2  2  2  0  0  0  0  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+63x^14+136x^15+236x^16+344x^17+581x^18+884x^19+1156x^20+1336x^21+1190x^22+932x^23+592x^24+360x^25+202x^26+92x^27+60x^28+8x^29+11x^30+4x^31+3x^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 1.04 seconds.