The generator matrix

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

generates a code of length 21 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+52x^12+60x^13+140x^14+192x^15+368x^16+612x^17+1199x^18+1812x^19+2325x^20+2796x^21+2344x^22+1892x^23+1212x^24+588x^25+374x^26+188x^27+126x^28+40x^29+36x^30+12x^31+11x^32+3x^34+1x^36

The gray image is a linear code over GF(2) with n=84, k=14 and d=24.
This code was found by Heurico 1.16 in 2.19 seconds.