The generator matrix

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

generates a code of length 60 over Z2[X]/(X^4) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+396x^52+1582x^53+3729x^54+7938x^55+12930x^56+20014x^57+29473x^58+35778x^59+38120x^60+36156x^61+29395x^62+20778x^63+13167x^64+7138x^65+3181x^66+1448x^67+586x^68+194x^69+68x^70+40x^71+10x^72+4x^73+10x^74+2x^75+6x^76

The gray image is a linear code over GF(2) with n=480, k=18 and d=208.
This code was found by Heurico 1.16 in 476 seconds.