The generator matrix

 1  1  1  1  1  1  1  1  X  0  1  1  1  X  1 X^3+X^2  1 X^2  X  1  1
 0  X  0 X^3+X^2+X X^2 X^2+X X^3+X^2  X X^2+X  X X^2+X  X X^2+X X^3+X^2+X X^2+X  X X^3+X^2 X^2 X^3+X^2+X X^2+X  0
 0  0 X^3+X^2  0 X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3
 0  0  0 X^3+X^2  0  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^2 X^3  0 X^3
 0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0 X^3  0 X^3 X^3  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+27x^16+114x^17+190x^18+452x^19+811x^20+940x^21+811x^22+416x^23+174x^24+114x^25+20x^26+12x^27+11x^28+3x^30

The gray image is a linear code over GF(2) with n=168, k=12 and d=64.
This code was found by Heurico 1.16 in 0.079 seconds.