The generator matrix

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

generates a code of length 21 over Z2[X]/(X^4) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+25x^18+16x^19+49x^20+352x^21+26x^22+16x^23+13x^24+13x^26+1x^36

The gray image is a linear code over GF(2) with n=168, k=9 and d=72.
This code was found by Heurico 1.16 in -6.48e-008 seconds.