The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^3  1  1  1 X^3
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X  0 X^2+X X^3+X^2 X^3+X X^3  X X^3+X^2 X^3+X^2+X  X  0 X^2+X X^2+X X^3+X^2 X^3 X^3+X X^2 X^3+X X^2+X X^2+X  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X X^3
 0  0 X^3+X^2  0 X^3+X^2 X^2  0 X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^2 X^3+X^2 X^2  0  0 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^2 X^3 X^3 X^3+X^2  0 X^3+X^2 X^3  0  0
 0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  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+566x^32+32x^34+336x^36+32x^38+56x^40+1x^64

The gray image is a linear code over GF(2) with n=272, k=10 and d=128.
This code was found by Heurico 1.16 in 0.047 seconds.