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.