The generator matrix

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

generates a code of length 26 over Z2[X]/(X^3) who´s minimum homogenous weight is 18.

Homogenous weight enumerator: w(x)=1x^0+38x^18+26x^19+103x^20+96x^21+480x^22+320x^23+1437x^24+592x^25+2040x^26+564x^27+1434x^28+320x^29+476x^30+112x^31+81x^32+16x^33+34x^34+2x^35+15x^36+4x^38+1x^40

The gray image is a linear code over GF(2) with n=104, k=13 and d=36.
This code was found by Heurico 1.16 in 12.4 seconds.