The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X  1 X^3  X  1  X  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^3+X X^3  0 X^2+X X^3+X^2 X^3+X^2+X X^3+X^2  X X^2+X  0 X^2+X X^2 X^3+X X^3+X X^3 X^3+X^2 X^2+X X^3+X^2 X^3+X  0  0 X^2+X X^3+X X^3 X^3+X^2 X^3+X^2+X  0  X X^3+X^2  0 X^2 X^3+X^2+X  X X^3+X^2 X^3+X^2+X X^3+X^2+X X^3+X X^3 X^3+X  0 X^3  0 X^3+X^2+X X^2 X^3+X^2  X X^2+X  X  X X^3+X^2+X X^3+X^2+X X^3+X^2+X X^3
 0  0 X^3+X^2  0 X^2 X^2  0 X^2 X^3 X^2  0  0 X^3 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^2 X^3  0 X^2  0  0 X^3+X^2 X^3+X^2 X^2  0  0 X^3 X^2 X^3 X^2 X^3  0 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^2  0 X^3+X^2 X^2  0  0 X^2 X^2 X^3 X^2 X^3
 0  0  0 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  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  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  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+44x^56+110x^57+130x^58+90x^59+418x^60+532x^61+397x^62+68x^63+99x^64+62x^65+46x^66+18x^67+14x^68+16x^69+2x^70+1x^110

The gray image is a linear code over GF(2) with n=488, k=11 and d=224.
This code was found by Heurico 1.16 in 0.328 seconds.