The generator matrix

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

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+161x^26+200x^28+347x^30+170x^32+103x^34+12x^36+29x^38+1x^48

The gray image is a linear code over GF(2) with n=120, k=10 and d=52.
This code was found by Heurico 1.16 in 12.9 seconds.