The generator matrix

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

generates a code of length 34 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+104x^24+88x^26+16x^27+520x^28+176x^29+1152x^30+656x^31+2715x^32+1200x^33+3152x^34+1200x^35+2688x^36+656x^37+1152x^38+176x^39+526x^40+16x^41+88x^42+88x^44+12x^48+2x^56

The gray image is a linear code over GF(2) with n=136, k=14 and d=48.
This code was found by Heurico 1.16 in 4.92 seconds.