The generator matrix

 1  1  1  1  1  1  1  1  X  X  X  1  1  X X^2 X^2 X^2  X  X X^2  X
 0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0  0
 0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  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+8x^20+44x^21+4x^22+3x^24+4x^25

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 6.87e-008 seconds.