The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 19.

Homogenous weight enumerator: w(x)=1x^0+68x^19+381x^20+816x^21+1658x^22+2542x^23+3603x^24+4724x^25+4992x^26+4812x^27+3839x^28+2658x^29+1554x^30+630x^31+300x^32+120x^33+52x^34+12x^35+4x^36+2x^37

The gray image is a linear code over GF(2) with n=104, k=15 and d=38.
This code was found by Heurico 1.16 in 10.9 seconds.