The generator matrix

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

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+44x^25+64x^26+96x^27+100x^28+122x^29+202x^30+130x^31+82x^32+72x^33+44x^34+28x^35+8x^36+18x^37+10x^38+2x^39+1x^48

The gray image is a linear code over GF(2) with n=120, k=10 and d=50.
This code was found by Heurico 1.16 in 0.894 seconds.