The generator matrix

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

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+89x^18+212x^19+618x^20+224x^21+611x^22+200x^23+82x^24+3x^26+4x^27+2x^28+1x^30+1x^32

The gray image is a linear code over GF(2) with n=168, k=11 and d=72.
This code was found by Heurico 1.16 in 0.016 seconds.