The generator matrix

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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+642x^55+2038x^56+4492x^57+6784x^58+11062x^59+13642x^60+18516x^61+17138x^62+18256x^63+13727x^64+11256x^65+6554x^66+4008x^67+1810x^68+750x^69+209x^70+104x^71+46x^72+24x^73+2x^74+6x^75+2x^77+2x^79+1x^86

The gray image is a linear code over GF(2) with n=496, k=17 and d=220.
This code was found by Heurico 1.16 in 291 seconds.