The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+404x^53+1750x^54+3806x^55+7987x^56+13242x^57+20564x^58+28286x^59+35669x^60+37612x^61+36323x^62+29442x^63+21315x^64+12780x^65+7162x^66+3222x^67+1573x^68+624x^69+211x^70+82x^71+43x^72+26x^73+4x^74+8x^75+4x^76+2x^78+2x^79

The gray image is a linear code over GF(2) with n=488, k=18 and d=212.
This code was found by Heurico 1.16 in 496 seconds.