The generator matrix

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

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+118x^56+288x^57+296x^58+576x^59+402x^60+800x^61+332x^62+672x^63+242x^64+192x^65+104x^66+32x^67+30x^68+4x^70+4x^72+1x^80+2x^88

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 0.328 seconds.