The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  X  1  1  X  X  1  2  2  1  X
 0  X  0  0  0  0  0  0  0  X X+2  X  X  X  2  X X+2  0  2  X X+2
 0  0  X  0  0  0  X X+2  X  0  0  2  2 X+2  2  X  0  X  X X+2 X+2
 0  0  0  X  0  X  X X+2  0  X  X  2  0  0 X+2  X X+2  0 X+2  2  2
 0  0  0  0  X  X  0 X+2  X  2 X+2 X+2 X+2  0  0  X X+2 X+2  0 X+2 X+2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2
 0  0  0  0  0  0  2  0  2  2  0  0  0  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  2  0  2  2  0  2  2  0  2  2  2  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+250x^14+8x^15+750x^16+176x^17+1734x^18+1016x^19+3379x^20+1696x^21+3354x^22+1016x^23+1966x^24+176x^25+626x^26+8x^27+172x^28+52x^30+3x^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 67.9 seconds.