The generator matrix
1 1 1 1 1 1 1 1 1 1 X 0 1 1 X 2 1 1 X 0 1
0 X 0 X 0 0 X X+2 2 0 2 2 X X+2 X X 2 0 X X 0
0 0 X X 0 X+2 X 2 0 0 X X X+2 2 X+2 X+2 X X X 0 0
0 0 0 2 0 0 2 0 0 2 0 2 0 2 2 0 2 0 2 0 0
0 0 0 0 2 0 0 0 2 2 0 2 2 2 0 2 0 2 2 2 0
0 0 0 0 0 2 2 2 2 0 0 2 0 0 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+36x^16+52x^17+84x^18+128x^19+143x^20+160x^21+140x^22+120x^23+63x^24+44x^25+28x^26+8x^27+13x^28+4x^30
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 0.0195 seconds.