The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2 X+2  1  1  X  1  1  0  X X+2  1
 0  1  0  1  X X+3  1  0 X+3  1  1  X X+1  2  1  1 X+2  1 X+2  1  0
 0  0  1  1  1  0 X+3  X  X  1  X  1 X+1  1  X X+3  3 X+1  2  1  0
 0  0  0  X  0 X+2 X+2  X  2  2  X X+2  0  0  2  X X+2  0 X+2  X  0
 0  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  0  0  0  2  0
 0  0  0  0  0  2  0  0  0  2  2  0  0  2  2  2  2  2  0  2  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  2  0  0  2  0  0  0  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+40x^14+140x^15+399x^16+648x^17+1201x^18+1964x^19+2498x^20+2712x^21+2365x^22+1892x^23+1275x^24+728x^25+355x^26+100x^27+49x^28+8x^29+7x^30+1x^32+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 1.83 seconds.