The generator matrix

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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+342x^54+1044x^55+1850x^56+3122x^57+3728x^58+4452x^59+4339x^60+4378x^61+3468x^62+2714x^63+1593x^64+968x^65+408x^66+160x^67+116x^68+42x^69+22x^70+14x^71+4x^72+2x^73+1x^76

The gray image is a linear code over GF(2) with n=480, k=15 and d=216.
This code was found by Heurico 1.16 in 11.1 seconds.