The generator matrix

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

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+82x^13+364x^14+1146x^15+2542x^16+5176x^17+9391x^18+15182x^19+20524x^20+22288x^21+20395x^22+15230x^23+9419x^24+5328x^25+2525x^26+1010x^27+343x^28+86x^29+29x^30+8x^31+2x^32+1x^36

The gray image is a linear code over GF(2) with n=84, k=17 and d=26.
This code was found by Heurico 1.13 in 32.4 seconds.