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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+125x^26+4x^27+404x^28+64x^29+685x^30+292x^31+1185x^32+672x^33+1403x^34+652x^35+1108x^36+288x^37+726x^38+76x^39+348x^40+127x^42+24x^44+5x^46+2x^48+1x^50

The gray image is a linear code over GF(2) with n=136, k=13 and d=52.
This code was found by Heurico 1.16 in 2.08 seconds.