The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1  1  1 X^2  1  1  1 X^2+X  1 X^2+X  1  1  0  1  1  1  1  X  1 X^2+X  1  1  1 X^2+X  1  1 X^2+X  1 X^2  1  1  1  1  1  0  X  0  0  1  1  0  1  0  1  1  1 X^2  0  1
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1 X^2 X^2+X+1  1  0 X^2+X X^2+1  1 X^2+1  1 X^2+X X+1  1 X^2+X X^2+X+1 X^2+X X^2+1  1 X^2  1 X^2+X+1  0 X^2+X  1  X X^2+X  1 X+1  1  1  X X^2+1 X^2+1  0  1  1  1  0 X^2+X+1  1  0 X^2+X  1 X^2+1 X^2+1 X^2+X+1  1  1 X+1
 0  0  X  0 X^2+X  0 X^2+X X^2  X  X  X X^2 X^2+X  X  X X^2 X^2+X X^2 X^2  X X^2+X  0  0  0  0 X^2+X X^2+X X^2+X  X X^2+X  0 X^2+X X^2  0  0 X^2+X X^2  0  0 X^2+X X^2  0 X^2 X^2+X  X X^2 X^2 X^2+X  X X^2 X^2  X  0 X^2  X X^2+X  X  0 X^2  0
 0  0  0 X^2  0  0  0 X^2 X^2  0 X^2  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 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2
 0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2  0  0 X^2  0  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2
 0  0  0  0  0  0 X^2  0 X^2  0  0  0 X^2 X^2  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 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0  0 X^2  0 X^2  0  0 X^2  0 X^2 X^2 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+78x^53+158x^54+274x^55+231x^56+478x^57+315x^58+496x^59+190x^60+484x^61+289x^62+408x^63+200x^64+204x^65+100x^66+92x^67+10x^68+30x^69+22x^70+6x^71+7x^72+6x^73+9x^74+4x^75+3x^78+1x^80

The gray image is a linear code over GF(2) with n=240, k=12 and d=106.
This code was found by Heurico 1.16 in 79.8 seconds.