The generator matrix

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

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+36x^24+24x^25+40x^26+72x^27+103x^28+160x^29+165x^30+160x^31+94x^32+72x^33+38x^34+24x^35+21x^36+7x^38+1x^40+5x^42+1x^50

The gray image is a linear code over GF(2) with n=120, k=10 and d=48.
This code was found by Heurico 1.16 in 0.0396 seconds.