The generator matrix

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

generates a code of length 21 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+332x^16+128x^17+844x^18+512x^19+1940x^20+768x^21+1772x^22+512x^23+1008x^24+128x^25+196x^26+44x^28+4x^30+3x^32

The gray image is a code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.16 in 6.34 seconds.