The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+88x^25+176x^26+242x^27+308x^28+470x^29+686x^30+910x^31+1533x^32+2348x^33+2760x^34+2392x^35+1624x^36+984x^37+620x^38+480x^39+325x^40+188x^41+104x^42+70x^43+44x^44+18x^45+6x^46+2x^47+4x^48+1x^56

The gray image is a linear code over GF(2) with n=136, k=14 and d=50.
This code was found by Heurico 1.16 in 9.89 seconds.