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

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+86x^19+188x^20+232x^21+272x^22+400x^23+724x^24+1308x^25+1722x^26+1368x^27+752x^28+384x^29+271x^30+248x^31+123x^32+60x^33+38x^34+10x^35+4x^36+1x^46

The gray image is a linear code over GF(2) with n=104, k=13 and d=38.
This code was found by Heurico 1.16 in 95.5 seconds.