The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  0  X  X  1  1  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2+X X^2+X  0  0  0  0  0 X^2 X^2
 0  0 X^2  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2
 0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0  0 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0 X^2 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+32x^15+64x^16+194x^18+224x^19+512x^20+512x^22+224x^23+188x^24+60x^26+32x^27+3x^32+2x^34

The gray image is a linear code over GF(2) with n=84, k=11 and d=30.
This code was found by Heurico 1.16 in 0.144 seconds.