The generator matrix

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

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+49x^30+390x^31+563x^32+696x^33+818x^34+694x^35+460x^36+274x^37+72x^38+32x^39+16x^40+22x^41+3x^42+4x^43+1x^46+1x^50

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 0.109 seconds.