The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+55x^20+52x^21+360x^22+252x^23+492x^24+476x^25+764x^26+440x^27+542x^28+268x^29+224x^30+44x^31+91x^32+4x^33+28x^34+3x^36

The gray image is a linear code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.243 seconds.