The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X X^2  0  0  0  X  1  X  1 X^2
 0  X  0  0  0  0  0  0  0  X X^2+X  X X^2 X^2  X  0 X^2 X^2+X  X X^2+X X^2  X  X X^2 X^2  X  X  X  X X^2
 0  0  X  0  0  0  X X^2+X  X  X  X  0  0  X X^2  X X^2+X X^2+X X^2 X^2 X^2+X X^2  X  0 X^2  0  0  0 X^2 X^2
 0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2 X^2 X^2+X X^2+X  0  X  0 X^2+X  0 X^2+X X^2  X  0  X X^2+X  X  X X^2
 0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  0 X^2+X  X X^2  X X^2+X  X X^2+X X^2+X X^2 X^2+X  0  X X^2+X X^2+X  0  X  0
 0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2  0  0 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+294x^24+56x^25+113x^26+272x^27+533x^28+720x^29+196x^30+640x^31+503x^32+312x^33+166x^34+48x^35+178x^36+36x^38+26x^40+1x^42+1x^44

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 35.9 seconds.