The generator matrix

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

generates a code of length 28 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+70x^20+78x^21+186x^22+226x^23+278x^24+372x^25+718x^26+1386x^27+1614x^28+1352x^29+692x^30+374x^31+273x^32+236x^33+185x^34+62x^35+68x^36+10x^37+10x^38+1x^50

The gray image is a linear code over GF(2) with n=112, k=13 and d=40.
This code was found by Heurico 1.16 in 1.63 seconds.