The generator matrix

 1  0  1  1  1 X^2  1  1 X^2  1  0  1 X^2  1 X^2+X X^2  1  1  1  1 X^2+X  1  1 X^2  X  1 X^2+X  0 X^2  1
 0  1  1  0  1  1 X+1 X^2  1 X+1  1 X^2+X  1  0  1  1 X+1  X  X  1  1 X^2+X+1 X+1  1  1 X^2+X  1  0  1  0
 0  0  X  0  0  0  0  0  0  X X^2 X^2 X^2+X X^2+X  X X^2+X X^2 X^2+X X^2+X  X X^2  X X^2  X X^2 X^2+X X^2  0 X^2  X
 0  0  0  X  0  X  X  0 X^2 X^2+X X^2+X X^2+X  0 X^2+X X^2 X^2+X X^2  0 X^2+X X^2+X  X X^2+X  0 X^2  0  0 X^2 X^2  0  X
 0  0  0  0  X X^2  X X^2+X  X  0  X X^2+X  0  0 X^2+X X^2  0 X^2 X^2+X X^2+X X^2  X  0  X X^2 X^2+X X^2  X X^2+X  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+48x^24+164x^25+181x^26+428x^27+317x^28+716x^29+442x^30+672x^31+354x^32+412x^33+126x^34+140x^35+43x^36+20x^37+18x^38+8x^39+5x^40+1x^42

The gray image is a linear code over GF(2) with n=120, k=12 and d=48.
This code was found by Heurico 1.16 in 0.304 seconds.