The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+107x^16+16x^17+224x^18+128x^19+479x^20+224x^21+386x^22+128x^23+219x^24+16x^25+92x^26+25x^28+2x^30+1x^32

The gray image is a linear code over GF(2) with n=84, k=11 and d=32.
This code was found by Heurico 1.16 in 0.0652 seconds.