The generator matrix
1 1 1 1 1 1 1 1 X X X 1 1 1 1
0 X 0 X 0 0 X X^2+X X X^2+X X^2 X^2 X^2+X X^2 X
0 0 X X 0 X^2+X X 0 X 0 X X X X^2+X X^2+X
0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 X^2 0 X^2
0 0 0 0 X^2 0 0 0 0 X^2 X^2 X^2 0 X^2 0
0 0 0 0 0 X^2 0 0 X^2 X^2 0 0 X^2 X^2 0
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+73x^10+167x^12+192x^13+265x^14+640x^15+288x^16+192x^17+163x^18+53x^20+11x^22+3x^24
The gray image is a linear code over GF(2) with n=60, k=11 and d=20.
This code was found by Heurico 1.16 in 8.94 seconds.