The generator matrix

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

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+29x^14+242x^15+529x^16+1334x^17+2069x^18+4462x^19+4521x^20+6298x^21+4597x^22+4542x^23+2055x^24+1370x^25+469x^26+162x^27+59x^28+22x^29+2x^30+3x^32+2x^34

The gray image is a linear code over GF(2) with n=84, k=15 and d=28.
This code was found by Heurico 1.16 in 6.42 seconds.