The generator matrix

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

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+132x^53+351x^54+574x^55+657x^56+660x^57+803x^58+598x^59+922x^60+706x^61+652x^62+502x^63+532x^64+394x^65+283x^66+168x^67+128x^68+90x^69+21x^70+10x^71+2x^73+2x^75+2x^78+2x^79

The gray image is a linear code over GF(2) with n=240, k=13 and d=106.
This code was found by Heurico 1.16 in 2.58 seconds.