The generator matrix

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

generates a code of length 15 over Z2[X]/(X^3) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+72x^11+116x^12+376x^13+122x^14+640x^15+203x^16+384x^17+36x^18+56x^19+32x^20+8x^21+2x^22

The gray image is a linear code over GF(2) with n=60, k=11 and d=22.
This code was found by Heurico 1.16 in 1.42 seconds.