The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1 1 X X 1 X^2 X^2 1 X
0 X 0 0 0 0 0 0 0 X X^2+X X X X X^2 X X^2+X 0 X^2 X X^2+X
0 0 X 0 0 0 X X^2+X X 0 0 X^2 X^2 X^2+X X^2 X 0 X X X^2+X X^2+X
0 0 0 X 0 X X X^2+X 0 X X X^2 0 0 X^2+X X X^2+X 0 X^2+X X^2 X^2
0 0 0 0 X X 0 X^2+X X X^2 X^2+X X^2+X X^2+X 0 0 X X^2+X X^2+X 0 X^2+X X^2+X
0 0 0 0 0 X^2 0 0 0 0 0 0 0 0 0 X^2 X^2 X^2 X^2 X^2 X^2
0 0 0 0 0 0 X^2 0 X^2 X^2 0 0 0 0 X^2 X^2 X^2 X^2 0 0 X^2
0 0 0 0 0 0 0 X^2 X^2 0 X^2 X^2 0 X^2 X^2 0 X^2 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 14.
Homogenous weight enumerator: w(x)=1x^0+250x^14+8x^15+750x^16+176x^17+1734x^18+1016x^19+3379x^20+1696x^21+3354x^22+1016x^23+1966x^24+176x^25+626x^26+8x^27+172x^28+52x^30+3x^32+1x^36
The gray image is a linear code over GF(2) with n=84, k=14 and d=28.
This code was found by Heurico 1.16 in 66.8 seconds.