The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  X  1  1  1 X^2  1  1  1  1
 0  X  0  X  0 X^2  X X^2+X  0 X^2  X X^2+X  0  0 X^2+X X^2+X X^2 X^2  X  0 X^2+X X^2  0  0  0  X X^2+X X^2  X  X
 0  0  X  X  0  X X^2+X X^2  0  X  X  0  0 X^2+X  X X^2  X X^2 X^2  X  0  0 X^2+X X^2 X^2  X  X X^2+X  0  X
 0  0  0 X^2  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0  0  0  0 X^2 X^2  0 X^2 X^2 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+20x^26+42x^27+88x^28+36x^29+185x^30+16x^31+68x^32+20x^33+10x^34+6x^35+1x^36+8x^37+9x^38+1x^40+1x^52

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 0.0169 seconds.