The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+535x^54+2020x^55+4341x^56+7040x^57+10823x^58+14072x^59+17582x^60+18024x^61+18140x^62+14200x^63+10940x^64+6980x^65+3505x^66+1656x^67+774x^68+240x^69+146x^70+20x^71+24x^72+4x^73+2x^74+2x^76+1x^86

The gray image is a linear code over GF(2) with n=488, k=17 and d=216.
This code was found by Heurico 1.16 in 139 seconds.