The generator matrix

 1  0  0  1  1  1 X^3+X^2+X X^3  1  1 X^3  1  1  1 X^3+X^2 X^2+X X^3+X^2  X  1 X^3+X^2  1
 0  1  0  1  X X^2+X+1  1  1  X X^3+X  1 X^3+X^2+X+1  1 X^3+X^2  X  1  1  0 X+1  1  0
 0  0  1  1  1  0  1  X X+1 X^3 X^2+1 X^2+X+1  X X^3+X  1 X^3+X^2 X^3+X^2+1  1 X^2+1 X^3+X+1  0
 0  0  0  X X^3 X^3+X X^2+X X^2+X  X X^2+X X^2 X^2  0 X^3+X X^3+X X^3+X X^3+X^2+X X^3+X X^3+X X^2  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+92x^16+550x^17+1621x^18+3696x^19+6208x^20+8166x^21+6706x^22+3680x^23+1347x^24+530x^25+137x^26+16x^27+14x^28+2x^29+2x^32

The gray image is a linear code over GF(2) with n=168, k=15 and d=64.
This code was found by Heurico 1.16 in 2.84 seconds.