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.