The generator matrix

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

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+58x^16+100x^18+64x^19+236x^20+128x^21+200x^22+64x^23+136x^24+20x^26+12x^28+5x^32

The gray image is a code over GF(2) with n=84, k=10 and d=32.
This code was found by Heurico 1.16 in 0.0202 seconds.