The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+292x^55+1179x^56+1962x^57+2717x^58+3882x^59+4342x^60+4484x^61+4542x^62+3486x^63+2445x^64+1790x^65+846x^66+382x^67+246x^68+64x^69+54x^70+38x^71+11x^72+4x^73+1x^74

The gray image is a linear code over GF(2) with n=488, k=15 and d=220.
This code was found by Heurico 1.16 in 11.4 seconds.