The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+292x^53+1007x^54+1786x^55+3216x^56+3606x^57+4571x^58+4370x^59+4462x^60+3448x^61+2952x^62+1486x^63+829x^64+398x^65+187x^66+78x^67+38x^68+16x^69+11x^70+8x^71+6x^72

The gray image is a linear code over GF(2) with n=472, k=15 and d=212.
This code was found by Heurico 1.16 in 11.2 seconds.