The generator matrix

 1  0  1  1  1  0  1  1 X^2  1  1 X^2+X  X  1 X^2+X  1  1  1 X^2  1  X
 0  1  1  0 X+1  1 X^2+X+1  0  1 X^2 X^2+1  1  1 X^2+X  1 X^2+1  0  0  X  X X^2+X
 0  0  X  0  0  0  0  X  X X^2+X X^2+X X^2 X^2+X X^2  X X^2+X X^2+X X^2+X X^2+X  X  X
 0  0  0  X  0 X^2+X X^2+X  X X^2 X^2  X X^2  0  0 X^2+X X^2+X  X  X  0  0 X^2+X
 0  0  0  0 X^2  0  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2 X^2 X^2  0 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 15.

Homogenous weight enumerator: w(x)=1x^0+78x^15+222x^16+294x^17+534x^18+950x^19+1318x^20+1438x^21+1238x^22+970x^23+598x^24+306x^25+146x^26+50x^27+34x^28+10x^29+2x^30+3x^32

The gray image is a linear code over GF(2) with n=84, k=13 and d=30.
This code was found by Heurico 1.16 in 87.8 seconds.