The generator matrix

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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+68x^56+282x^57+430x^58+504x^59+414x^60+746x^61+449x^62+546x^63+318x^64+176x^65+72x^66+36x^67+28x^68+10x^69+5x^70+2x^71+3x^72+2x^73+3x^74+1x^90

The gray image is a linear code over GF(2) with n=488, k=12 and d=224.
This code was found by Heurico 1.16 in 0.375 seconds.