The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+132x^52+148x^53+382x^54+348x^55+552x^56+656x^57+714x^58+944x^59+689x^60+812x^61+682x^62+668x^63+449x^64+408x^65+258x^66+88x^67+109x^68+24x^69+64x^70+46x^72+12x^74+5x^76+1x^84

The gray image is a linear code over GF(2) with n=240, k=13 and d=104.
This code was found by Heurico 1.16 in 4.02 seconds.