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^2  1 X^2  1  X  X  1  1  X  X  1  X  1  X  0  1  X  1  1  1  X  1  1  1 X^2  1  1  1
 0  X  0  0  0  0  0  0 X^2  X X^2+X X^2+X  X  X  X  X X^2  0 X^2 X^2  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X X^2  0  0 X^2  X  X X^2  X X^2+X X^2+X  X X^2 X^2+X X^2+X X^2+X  0  X X^2  0  0 X^2+X  X X^2+X  0  0  0 X^2+X  X X^2  0 X^2 X^2 X^2
 0  0  X  0  0  0  X X^2+X X^2+X  X  X X^2  X  X X^2+X  0 X^2 X^2 X^2+X  X X^2  X  0 X^2  X X^2  0  X  0  X  0 X^2+X X^2+X X^2+X  X  X  X  X  0 X^2 X^2+X X^2+X  0  X X^2+X  X  X  0  X  X  X X^2  0 X^2  0 X^2  X X^2 X^2+X  X
 0  0  0  X  0  X  X  X  0 X^2  0  X X^2+X X^2+X X^2  0 X^2+X X^2 X^2+X  0 X^2+X X^2 X^2 X^2+X  X  0 X^2+X X^2  X X^2+X  0 X^2+X  0 X^2+X X^2+X X^2 X^2  X  X  X X^2+X  X X^2 X^2+X  0 X^2+X X^2 X^2 X^2+X X^2+X X^2  0 X^2+X  X X^2 X^2+X X^2  0 X^2+X X^2+X
 0  0  0  0  X  X X^2 X^2+X  X X^2  X  0  X  0  X  0 X^2  0  X X^2+X X^2+X X^2  X X^2  X X^2+X X^2+X X^2 X^2+X X^2 X^2+X  0  0  0  X  0  X X^2+X X^2  X X^2 X^2 X^2+X  0  X  0  0 X^2+X  X X^2 X^2  X  0  X  0 X^2+X X^2 X^2+X X^2 X^2
 0  0  0  0  0 X^2 X^2 X^2  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2 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+127x^52+308x^54+24x^55+415x^56+200x^57+488x^58+240x^59+530x^60+400x^61+488x^62+120x^63+298x^64+40x^65+168x^66+133x^68+68x^70+29x^72+16x^74+2x^76+1x^96

The gray image is a linear code over GF(2) with n=240, k=12 and d=104.
This code was found by Heurico 1.16 in 1.24 seconds.