The generator matrix

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

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+10x^16+76x^17+146x^18+182x^19+351x^20+522x^21+396x^22+180x^23+77x^24+40x^25+34x^26+22x^27+9x^28+2x^29

The gray image is a linear code over GF(2) with n=168, k=11 and d=64.
This code was found by Heurico 1.16 in 0.031 seconds.