The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  1  0  1  0 X^2  1  1  X  1 X^2 X^2  0  1 X^2  X  0  1  1  X
 0  X  0  X  0  0  X X^2+X  0  0  X X^2+X X^2  X X^2+X  0  X  0 X^2  X X^2+X  X  0  X  X  X  X  0  X  X X^2 X^2  0  0
 0  0  X  X  0 X^2+X  X  0  0 X^2+X  X X^2  X X^2+X  0 X^2+X X^2  0  X X^2+X  0  X X^2+X X^2+X  X  X  0 X^2+X X^2+X X^2+X  X X^2+X X^2+X  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2
 0  0  0  0  0 X^2  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  0  0  0  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2
 0  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 X^2 X^2 X^2 X^2  0  0 X^2
 0  0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0  0 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+136x^24+218x^26+16x^27+759x^28+176x^29+1274x^30+656x^31+2415x^32+1200x^33+2628x^34+1200x^35+2476x^36+656x^37+1332x^38+176x^39+732x^40+16x^41+162x^42+124x^44+18x^46+12x^48+1x^60

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 7.52 seconds.