The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2  X  0  0  0  1  1  X  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  0  X X^2+X  X X^2+X X^2+X  0 X^2+X X^2+X  X  X  0  X  X  X X^2+X X^2+X X^2+X  X
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X X^2+X  X  X X^2  0  X  0  X X^2 X^2 X^2+X  X X^2  X  X X^2+X X^2+X  X X^2+X
 0  0  0  X  X  0 X^2+X  X X^2 X^2+X  X X^2 X^2  X  X X^2  0 X^2 X^2  X  X  0 X^2  0  X X^2  X  0 X^2 X^2
 0  0  0  0 X^2  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 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  0  0  0 X^2  0 X^2  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 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+225x^24+356x^26+32x^27+640x^28+480x^29+644x^30+480x^31+650x^32+32x^33+364x^34+128x^36+44x^38+19x^40+1x^48

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 18 seconds.