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.