The generator matrix
1 1 1 1 1 1 1 1 1 1 X X 1 1 1
0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0
0 0 X^2 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 X^2
0 0 0 X^2 0 0 0 X^2 0 X^2 0 X^2 0 X^2 X^2
0 0 0 0 X^2 0 0 X^2 0 0 X^2 X^2 X^2 X^2 0
0 0 0 0 0 X^2 0 X^2 X^2 0 X^2 0 X^2 0 X^2
0 0 0 0 0 0 X^2 X^2 X^2 0 0 X^2 0 0 X^2
generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+17x^10+28x^12+32x^13+20x^14+320x^15+21x^16+32x^17+22x^18+12x^20+4x^22+2x^24+1x^26
The gray image is a linear code over GF(2) with n=60, k=9 and d=20.
This code was found by Heurico 1.16 in 0.00313 seconds.