The generator matrix

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

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+16x^54+170x^55+124x^56+482x^57+376x^58+636x^59+517x^60+644x^61+358x^62+434x^63+123x^64+186x^65+12x^66+8x^67+2x^68+1x^70+4x^74+1x^76+1x^86

The gray image is a linear code over GF(2) with n=480, k=12 and d=216.
This code was found by Heurico 1.16 in 0.313 seconds.