The generator matrix

 1  0  1  1  1 X^3+X^2+X  1  X  1 X^3  1  1 X^2  1  1  1 X^2+X  1  1 X^3+X^2  1 X^3+X  1  1  1  1  1  1  0  1 X^2+X  1 X^2+X  1  1  X  1 X^2 X^3+X^2+X X^3+X^2  0  1  1  1  1  X  1  1  1  1  0  X  1 X^3+X^2  1  1  1  1  1  1
 0  1 X+1 X^2+X X^3+X^2+1  1 X^3+X^2  1 X^2+X+1  1 X^3+X  1  1 X^3 X+1 X^3+X^2+X  1 X^3+X^2+X+1 X^2  1  X  1 X+1 X^3+X^2+X+1 X^2+1 X^3+1 X^2+1  0  1 X^3+X  1 X^2+X  1 X^3+X^2+X+1 X^3+X^2+1 X^2 X^3+1  1  1  1  X X^3+X^2+1 X^3  1 X^2+X+1  1 X^3 X^3+X X^3+X X^3+X^2  1 X^2 X^2+X+1  X  1 X^3+1 X^2+1 X^3+X^2+1 X^2+1  0
 0  0 X^2  0 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^2 X^3 X^3+X^2  0 X^3 X^2  0 X^3+X^2  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2  0 X^2 X^2 X^3+X^2  0  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^2  0  0  0 X^3 X^2 X^3+X^2  0
 0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+60x^55+320x^56+376x^57+573x^58+396x^59+763x^60+490x^61+421x^62+234x^63+300x^64+86x^65+27x^66+12x^67+17x^68+2x^69+2x^71+4x^72+6x^73+2x^74+2x^76+1x^78+1x^80

The gray image is a linear code over GF(2) with n=480, k=12 and d=220.
This code was found by Heurico 1.16 in 0.375 seconds.