The generator matrix

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

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+48x^24+12x^25+171x^26+128x^27+330x^28+516x^29+786x^30+1296x^31+1671x^32+2120x^33+2174x^34+2160x^35+1668x^36+1336x^37+820x^38+496x^39+324x^40+108x^41+132x^42+16x^43+50x^44+4x^45+10x^46+4x^48+2x^50+1x^58

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 5.05 seconds.