The generator matrix
1 1 1 1 X 1 1 0 X 1 1 X X 1 1
0 X 0 X^2+X X 0 X^2+X X X^2+X 0 X^2+X X^2+X 0 0 0
0 0 X^2 0 0 0 0 0 0 X^2 0 X^2 X^2 0 0
0 0 0 X^2 0 0 0 0 X^2 X^2 0 X^2 0 0 0
0 0 0 0 X^2 0 0 0 X^2 0 0 X^2 X^2 0 0
0 0 0 0 0 X^2 0 0 0 X^2 X^2 X^2 0 0 0
0 0 0 0 0 0 X^2 0 X^2 X^2 X^2 0 0 0 0
0 0 0 0 0 0 0 X^2 X^2 0 X^2 0 X^2 0 0
generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+46x^8+48x^10+261x^12+648x^14+725x^16+192x^18+106x^20+8x^22+12x^24+1x^28
The gray image is a linear code over GF(2) with n=60, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0138 seconds.