The generator matrix

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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+96x^25+331x^26+386x^27+547x^28+438x^29+597x^30+416x^31+524x^32+340x^33+221x^34+90x^35+77x^36+22x^37+3x^38+4x^39+3x^40

The gray image is a linear code over GF(2) with n=120, k=12 and d=50.
This code was found by Heurico 1.11 in 0.093 seconds.