The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+76x^12+16x^13+60x^14+470x^16+832x^17+500x^18+2560x^19+928x^20+5472x^21+944x^22+2560x^23+520x^24+832x^25+480x^26+52x^28+16x^29+52x^30+1x^32+12x^34

The gray image is a code over GF(2) with n=84, k=14 and d=24.
This code was found by Heurico 1.16 in 1.2 seconds.