The generator matrix

 1  0  0  1  1  1  0  1 X^2  1  X  1  1 X^2+X  1 X^2  0  1 X^2+X  1  1  1 X^2+X  X X^2+X  1  1 X^2+X  0  1
 0  1  0  0  1 X^2+1  1  X  1 X+1  1  X X^2+1  0  1 X^2+X  1 X^2+1  1 X^2 X^2+X  1  1  1  1 X^2 X^2+X+1  1  1  1
 0  0  1 X+1 X^2+X+1  0 X+1 X^2+1 X^2+X X^2  1 X^2+X  1  1 X^2+X  1 X+1 X+1  X X^2+1  0 X^2+X  1  1 X^2+X+1  X X^2+1 X^2 X^2+X X^2
 0  0  0 X^2  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0 X^2
 0  0  0  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0  0 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+159x^26+188x^27+380x^28+228x^29+299x^30+192x^31+244x^32+112x^33+138x^34+36x^35+46x^36+12x^37+11x^38+1x^40+1x^42

The gray image is a linear code over GF(2) with n=120, k=11 and d=52.
This code was found by Heurico 1.16 in 0.0967 seconds.