The generator matrix

 1  0  0  0  1  1  1  1 X^2+X  1 X^2+X  1  0 X^2+X  1
 0  1  0  0  0  1 X^2+X+1 X^2 X^2 X+1  1 X^2+X  1 X^2+X X+1
 0  0  1  0  1  1  X X^2+X  1  X  1 X^2+1 X^2+X  1 X^2+X
 0  0  0  1  1  0 X^2  1 X^2+X+1 X+1 X+1 X^2 X^2+X+1  X  X
 0  0  0  0  X X^2 X^2  0 X^2 X^2+X X^2+X  X X^2+X  0  X

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+117x^10+516x^11+986x^12+1874x^13+2988x^14+3376x^15+2998x^16+1980x^17+989x^18+412x^19+108x^20+34x^21+2x^22+3x^24

The gray image is a linear code over GF(2) with n=60, k=14 and d=20.
This code was found by Heurico 1.13 in 0.422 seconds.