The generator matrix

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

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+162x^16+356x^17+725x^18+864x^19+1395x^20+1126x^21+1439x^22+954x^23+741x^24+240x^25+139x^26+36x^27+5x^28+6x^29+1x^30+2x^31

The gray image is a linear code over GF(2) with n=84, k=13 and d=32.
This code was found by Heurico 1.11 in 0.219 seconds.