The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  X  1 X^2  1  1  1  1  X  0  0  1  1  X
 0  X  0  X  0  0  X X^2+X  0 X^2  X X^2+X  0 X^2+X X^2  X  X  X X^2+X  X  X  X  0  0 X^2 X^2  X  0 X^2+X X^2
 0  0  X  X  0 X^2+X  X  0 X^2  X  X  0 X^2 X^2+X  X  X  X X^2+X  0 X^2+X  X  0 X^2+X X^2  X  X X^2  0 X^2 X^2
 0  0  0 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0  0 X^2 X^2
 0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2 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 24.

Homogenous weight enumerator: w(x)=1x^0+84x^24+207x^26+64x^27+318x^28+192x^29+352x^30+192x^31+303x^32+64x^33+182x^34+48x^36+24x^38+12x^40+3x^42+2x^44

The gray image is a linear code over GF(2) with n=120, k=11 and d=48.
This code was found by Heurico 1.16 in 0.118 seconds.