The generator matrix

 1  0  0  0  0  1  1  1 X^2+X  1  1 X^2+X  1  X X^2+X  1  0  0  1  1  1  1  1  1  1  1
 0  1  0  0  0  0 X^2  0 X^2 X+1  1  1 X^2+X+1 X^2+X  1 X+1  1  1 X^2+1 X+1 X^2+X X^2 X^2+X X+1 X^2+1  1
 0  0  1  0  0  0  1  1  1 X^2+1 X^2+X+1 X^2 X+1  1  X  X X^2+X+1 X^2+1 X^2+1 X^2+X  X X^2+X  X  0 X^2+1  X
 0  0  0  1  0  1  1  X X^2+X+1 X^2 X^2+X+1  1 X^2+1 X^2+1 X+1  1  1 X^2+X+1  0  X X^2+X+1 X^2+X+1 X^2 X^2+X  1 X^2
 0  0  0  0  1  1  X X+1 X+1 X^2+1 X+1 X^2+X+1  X X^2  X X+1  1 X^2 X^2+X  0 X+1  X X^2+X+1  0 X^2+1  X
 0  0  0  0  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0  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+234x^19+731x^20+1716x^21+3025x^22+5180x^23+7204x^24+8988x^25+10560x^26+9748x^27+7802x^28+5088x^29+2782x^30+1516x^31+571x^32+268x^33+80x^34+26x^35+11x^36+4x^37+1x^38

The gray image is a linear code over GF(2) with n=104, k=16 and d=38.
This code was found by Heurico 1.13 in 14.5 seconds.