The generator matrix

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

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+50x^15+324x^16+710x^17+1241x^18+1908x^19+2492x^20+2818x^21+2618x^22+2034x^23+1209x^24+578x^25+269x^26+88x^27+38x^28+6x^29

The gray image is a linear code over GF(2) with n=84, k=14 and d=30.
This code was found by Heurico 1.13 in 0.781 seconds.