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

generates a code of length 30 over Z2[X]/(X^3) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+31x^26+48x^27+50x^28+86x^29+95x^30+84x^31+51x^32+24x^33+17x^34+12x^35+10x^36+2x^37+1x^54

The gray image is a linear code over GF(2) with n=120, k=9 and d=52.
This code was found by Heurico 1.16 in 0.0145 seconds.