The generator matrix

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

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+61x^56+228x^57+498x^58+478x^59+642x^60+408x^61+551x^62+476x^63+469x^64+160x^65+55x^66+34x^67+14x^68+4x^69+5x^70+4x^71+4x^72+2x^78+1x^82+1x^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.