The generator matrix

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

generates a code of length 20 over Z2[X]/(X^3) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+242x^14+408x^15+1490x^16+1784x^17+4763x^18+3840x^19+7497x^20+4144x^21+4775x^22+1752x^23+1473x^24+344x^25+201x^26+16x^27+35x^28+3x^30

The gray image is a linear code over GF(2) with n=80, k=15 and d=28.
This code was found by Heurico 1.16 in 26.3 seconds.