The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  X  1  1  1 X^3+X^2  1  1 X^3  X  1  X  1
 0  1  0  0  0 X^3 X^2+1 X^3+X^2+X+1  1  1 X^2+X X^3+1 X^2+X+1  X X^2+1 X^3+X^2+X+1  1  1 X^3+X^2  1 X^2
 0  0  1  0  1 X^3+X^2+X X^2  X X^3+X X^2+1 X^2+X+1  1 X^3+1  1 X^2+X X+1 X^2+X X^3+1 X^3+X^2+X X^3+X^2+X+1 X^2
 0  0  0  1  1 X+1 X^2+X+1 X^2 X^3+X^2+X+1  1  X X^3+X X^3+X+1 X^2+X+1  0 X^3 X^3+X+1 X^3+X+1  X X^3 X^2+X
 0  0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 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+359x^16+1680x^17+5842x^18+14132x^19+26876x^20+32816x^21+27624x^22+14296x^23+5380x^24+1568x^25+450x^26+20x^27+24x^28+4x^30

The gray image is a linear code over GF(2) with n=168, k=17 and d=64.
This code was found by Heurico 1.16 in 31.9 seconds.