The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+86x^14+470x^15+1066x^16+2482x^17+4914x^18+7362x^19+10731x^20+11018x^21+11067x^22+7546x^23+4781x^24+2438x^25+1013x^26+398x^27+125x^28+30x^29+7x^30+1x^34

The gray image is a linear code over GF(2) with n=84, k=16 and d=28.
This code was found by Heurico 1.13 in 9.17 seconds.