The generator matrix

 1  0  0  0  1  1  1 X^3+X X^2+X  1  1 X^3  1  1  1 X^3+X^2 X^3+X^2+X  1  1  1  1
 0  1  0  0 X^2 X^3+1 X^2+1  1  1 X^2+X X^3+X  1 X+1 X^3+X^2+1 X^3+X+1 X^3  X X^3+X^2+X+1 X^2  X  0
 0  0  1  0 X^2+1  1 X^2 X^2+X+1  1 X+1  0 X^3+X  1 X^3+X^2+X+1 X^3+X^2+X+1  1  1 X^2+1 X^2+X+1 X+1  0
 0  0  0  1  1 X^2 X^2+X+1 X^2+X+1 X^3+X^2+X X^3 X^3+X^2+1  1 X^3+X^2+X+1 X^2+X  1 X^2+X X^2+X+1  X X^2+X+1 X^3+X  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+196x^16+1158x^17+3127x^18+7542x^19+12003x^20+17288x^21+12352x^22+7576x^23+2921x^24+1090x^25+239x^26+34x^27+5x^28+2x^30+2x^32

The gray image is a linear code over GF(2) with n=168, k=16 and d=64.
This code was found by Heurico 1.16 in 10.4 seconds.