The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+52x^53+131x^54+116x^55+88x^56+154x^57+210x^58+206x^59+201x^60+206x^61+192x^62+148x^63+78x^64+74x^65+84x^66+32x^67+14x^68+22x^69+19x^70+8x^71+4x^73+2x^74+2x^75+1x^76+2x^78+1x^96

The gray image is a linear code over GF(2) with n=240, k=11 and d=106.
This code was found by Heurico 1.16 in 18.6 seconds.