The generator matrix

 1  0  0  0  1  1  1  X  1  1 X^2+X X^2  1  1  X  1  X  0  1  1  1  1  X X^2+X  1  1  1  0  1 X^2+X  1  1 X^2+X X^2+X  1  1  1  X X^2+X  1  0 X^2  1  1  1 X^2+X X^2+X  1  0 X^2+X  1 X^2+X  1 X^2  1  X  0  1 X^2+X  1
 0  1  0  0  1  X  1  1 X^2 X^2+X  1  1 X^2+1 X+1  0 X+1  1  1 X^2+X X^2+1 X^2+1 X^2+1  X X^2  0  0 X^2 X^2+X X+1  1 X+1 X^2+X+1  1  1  X X+1 X^2+X+1  1  X  1  1  1 X^2+X+1 X^2 X+1  1  1  1  0 X^2+X  0  1 X+1  0 X^2+X  1  1 X^2+X X^2  0
 0  0  1  0  X  1 X+1  1  1 X^2 X^2+X+1  0 X+1  0  1  X  X X^2+1 X+1 X^2+1  X X^2+1  1  0 X^2 X^2+X X^2+1  1 X+1 X+1 X^2+X+1  0 X^2+X X^2+1 X^2 X^2+1  0  X  1 X^2 X^2+1  1 X^2+X+1 X+1  X  0  X  1  X  1  X X^2+X+1  0  1  X  1  1 X^2  1 X^2+1
 0  0  0  1  X X^2+X X^2 X^2+X  1  1 X+1 X^2+X+1  1 X^2+X+1 X+1 X+1  0 X^2+X X^2+X+1 X^2+1 X^2 X^2  1  1 X^2+X+1  0  X  0 X+1 X^2+X+1 X^2+X  X X^2+1  1 X+1  X X^2+X  0 X^2  1 X^2+1  0  0 X^2+X X^2 X+1  X X^2+X+1  1 X^2+X X+1 X^2+1 X^2+1  0  1 X^2  X X^2+X+1 X^2 X+1
 0  0  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  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+174x^53+310x^54+552x^55+592x^56+856x^57+625x^58+770x^59+668x^60+840x^61+600x^62+696x^63+414x^64+436x^65+241x^66+196x^67+74x^68+76x^69+40x^70+8x^71+11x^72+8x^74+2x^75+2x^77

The gray image is a linear code over GF(2) with n=240, k=13 and d=106.
This code was found by Heurico 1.11 in 0.953 seconds.