The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3  1  1 X^3+X  1  1 X^3+X^2  1  1 X^2 X^3  X  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^2+X+1 X^3  1 X^3+X X^2+1  1 X^3+X^2  1  1 X^3+X^2+X X+1  1  1  0 X^3
 0  0 X^2  0 X^3+X^2 X^3 X^2 X^3+X^2 X^2 X^3  0 X^3  0 X^2 X^3 X^3+X^2  0 X^2 X^2  0 X^2
 0  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 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+42x^17+158x^18+492x^19+945x^20+878x^21+916x^22+456x^23+135x^24+38x^25+14x^26+12x^27+7x^28+2x^29

The gray image is a linear code over GF(2) with n=168, k=12 and d=68.
This code was found by Heurico 1.16 in 0.297 seconds.