The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 X X X X^2 X 1 X X^2 X^2 X X^3 0 1 X^2 X^3 1
0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 0 X^3 X^3 0 X^3 X^3 0 X^3 0 X^3 0 X^3 X^3 0 0 X^3 0 0 X^3 X^3 X^3 0 0 0
generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 34.
Homogenous weight enumerator: w(x)=1x^0+1x^34+28x^35+1x^36+1x^38
The gray image is a linear code over GF(2) with n=272, k=5 and d=136.
This code was found by Heurico 1.16 in 0.015 seconds.