The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+42x^13+158x^14+226x^15+360x^16+684x^17+1266x^18+1786x^19+2236x^20+2646x^21+2466x^22+1902x^23+1196x^24+682x^25+366x^26+174x^27+108x^28+40x^29+32x^30+8x^31+3x^32+2x^33

The gray image is a linear code over GF(2) with n=84, k=14 and d=26.
This code was found by Heurico 1.16 in 3.11 seconds.