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

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+36x^52+58x^53+73x^54+60x^55+143x^56+144x^57+124x^58+266x^59+314x^60+260x^61+114x^62+136x^63+99x^64+32x^65+48x^66+36x^67+42x^68+18x^69+20x^70+12x^71+5x^72+4x^74+2x^75+1x^102

The gray image is a linear code over GF(2) with n=240, k=11 and d=104.
This code was found by Heurico 1.16 in 0.393 seconds.