The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  0  X X^3+X^2  X  0  X X^3+X^2  X  X  X X^3  X X^2  X X^3  X  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^3 X^3+X^2+X X^2 X^3+X X^3 X^3+X^2+X X^2  X X^2+X  X X^3+X  X X^2+X  X X^3+X  X  0 X^3+X^2 X^3+X^2+X  X  X  X X^3+X^2+X  X  0 X^3+X^2
 0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 32.

Homogenous weight enumerator: w(x)=1x^0+13x^32+72x^33+78x^34+80x^35+1x^36+8x^37+1x^38+1x^44+1x^46

The gray image is a linear code over GF(2) with n=272, k=8 and d=128.
This code was found by Heurico 1.16 in 0.031 seconds.