The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+86x^17+207x^18+290x^19+317x^20+292x^21+309x^22+268x^23+159x^24+70x^25+25x^26+18x^27+3x^28+3x^30

The gray image is a linear code over GF(2) with n=84, k=11 and d=34.
This code was found by Heurico 1.11 in 0.015 seconds.