The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+22x^13+102x^14+82x^15+254x^16+792x^17+1078x^18+2408x^19+1444x^20+3604x^21+2040x^22+2492x^23+836x^24+696x^25+344x^26+136x^27+12x^28+6x^29+18x^30+2x^31+13x^32+2x^34

The gray image is a linear code over GF(2) with n=84, k=14 and d=26.
This code was found by Heurico 1.16 in 47.8 seconds.