The generator matrix

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

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+40x^15+467x^16+400x^17+1488x^18+1496x^19+3007x^20+2272x^21+3142x^22+1496x^23+1540x^24+400x^25+374x^26+40x^27+104x^28+14x^30+2x^34+1x^36

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 2.66 seconds.