The generator matrix

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

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+19x^20+16x^21+19x^22+8x^23+1x^26

The gray image is a linear code over GF(2) with n=168, k=6 and d=80.
This code was found by Heurico 1.16 in 0 seconds.