The generator matrix

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

generates a code of length 34 over Z2[X]/(X^4) who´s minimum homogenous weight is 30.

Homogenous weight enumerator: w(x)=1x^0+106x^30+296x^31+664x^32+628x^33+796x^34+580x^35+621x^36+260x^37+91x^38+20x^39+15x^40+8x^41+6x^42+3x^44+1x^46

The gray image is a linear code over GF(2) with n=272, k=12 and d=120.
This code was found by Heurico 1.16 in 0.125 seconds.