The generator matrix

 1  1  1  1  1  1  1  1  X  1  0  1  1  1  1 X^3  1  1  X  1  X
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^3+X^2+X X^3  X X^3+X X^3+X^2 X^2+X  0  X  0 X^3+X^2 X^2+X  0 X^2+X
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3
 0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3  0
 0  0  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 17.

Homogenous weight enumerator: w(x)=1x^0+32x^17+134x^18+164x^19+449x^20+514x^21+437x^22+152x^23+120x^24+28x^25+4x^26+4x^27+5x^28+2x^29+1x^30+1x^32

The gray image is a linear code over GF(2) with n=168, k=11 and d=68.
This code was found by Heurico 1.16 in 0.031 seconds.