The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1
 0 X^2  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0
 0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0  0 X^2  0  0 X^2  0 X^2  0 X^2  0  0  0
 0  0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0  0  0
 0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0  0

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+84x^8+13x^10+280x^12+147x^14+630x^16+525x^18+2048x^19+8880x^20+2048x^21+715x^22+308x^24+463x^26+56x^28+161x^30+1x^32+23x^34+1x^38

The gray image is a linear code over GF(2) with n=80, k=14 and d=16.
This code was found by Heurico 1.16 in 0.822 seconds.