The generator matrix

 1  0  0  1  1  1  X  1  1  1  2 X+2  1  X  2 X+2  1  1  2  X  0
 0  1  0  1 X+2 X+3  1  0  0 X+1  1  1 X+3  X  X  0  X  X  X  1  1
 0  0  1  1 X+3 X+2  1 X+2 X+1 X+1  X X+1  X  1  1  1  X  1  1  X  0
 0  0  0  2  0  0  0  0  0  2  2  2  0  2  0  2  2  0  0  0  0
 0  0  0  0  2  0  0  0  2  0  2  2  0  2  2  0  0  0  2  2  2
 0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  2  2  2  2  2  0
 0  0  0  0  0  0  2  0  0  0  0  2  0  0  2  2  2  0  2  2  0
 0  0  0  0  0  0  0  2  2  2  2  0  2  2  0  0  2  2  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+48x^14+40x^15+369x^16+400x^17+1548x^18+1496x^19+3149x^20+2272x^21+3172x^22+1496x^23+1550x^24+400x^25+340x^26+40x^27+50x^28+12x^30+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 1.8 seconds.