The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  1  1  1 X^2 X^2  1  1 X^2  1  1  1
 0  1  1  0 X^2+X+1  1  X X^2+X+1  1  0 X+1 X^2  1  1  1 X^2+1 X^2+X  1 X^2+X  X  0
 0  0  X  0 X^2+X X^2  0  0 X^2+X  X X^2+X X^2+X X^2  0  X X^2  X  X  0 X^2+X  0
 0  0  0  X  0 X^2 X^2+X  X X^2  X  X X^2  0 X^2+X X^2 X^2 X^2+X  X  0 X^2  0
 0  0  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2  0 X^2  0 X^2 X^2  0 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+55x^16+84x^17+140x^18+250x^19+326x^20+360x^21+304x^22+254x^23+152x^24+68x^25+28x^26+6x^27+10x^28+8x^30+2x^31

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 0.0472 seconds.