The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+352x^57+415x^58+600x^59+421x^60+632x^61+480x^62+504x^63+272x^64+284x^65+63x^66+32x^67+9x^68+16x^69+12x^73+2x^78+1x^80

The gray image is a linear code over GF(2) with n=488, k=12 and d=228.
This code was found by Heurico 1.16 in 35.2 seconds.