The generator matrix

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

generates a code of length 60 over Z2[X]/(X^3) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+137x^54+168x^55+536x^56+328x^57+522x^58+352x^59+473x^60+240x^61+316x^62+244x^63+261x^64+128x^65+140x^66+64x^67+122x^68+8x^69+31x^70+4x^71+14x^72+6x^74+1x^76

The gray image is a linear code over GF(2) with n=240, k=12 and d=108.
This code was found by Heurico 1.16 in 0.747 seconds.