The generator matrix

 1  0  0  1  1  1  0 X^3+X^2 X^3+X^2 X^3+X^2  1  1  1  1 X^2+X X^3+X^2+X  1 X^3+X^2+X  1  X  1  1  1  1 X^2+X X^2+X  1  1 X^3+X^2+X  1  1 X^2 X^3+X  1  1  1 X^2 X^3+X  1  1 X^3+X^2  X  1 X^3+X^2 X^2  1  1  1  1 X^3+X^2+X X^3+X^2  1  1 X^2+X X^3+X^2 X^3+X^2  1 X^3+X^2+X  1 X^3+X^2 X^2+X
 0  1  0  0 X^2+1 X^3+X^2+1  1  X  1  1 X^3+X^2 X^2 X^2+1 X^2+1 X^3+X^2 X^3+X^2+X X+1  1 X^2+X  1  X X^2+X+1 X^3+X^2+X X^3+X^2+X+1  1  1  1  X  1 X^2 X+1  1 X^3 X^3+X X^3 X^3  1  1 X^3+X^2+X X^3+X^2+X+1 X^3+X  1  1  1  1 X^2+X+1  X X+1 X^3+X^2  1  1 X^2+X+1  0  1  0  0  X X^3+X^2+X X^2  1  1
 0  0  1 X+1 X^2+X+1 X^2 X^2+X+1  1  X X^3+1  X X^3+X^2+1 X^3+1 X^3+X^2+X  1  1 X^2+X X^3+X^2+1  1 X^3+X^2 X^2  0  X X+1 X^2+X X^2+X+1 X^3+X+1 X+1 X^3+X X^2 X^2+1 X^3+1  1  X X^3+X^2+1 X^3+X+1 X^3+X X^3+X^2+X+1  X X+1  1  X X^2+X X^3+X^2+X+1 X^3 X^3+X X^3+1 X^3+X^2 X^3+X  0 X^2+X X^3+X+1 X^2+X+1 X^3+X+1  1  1 X^2  1  1 X^3+X^2+1 X^3+X^2+X
 0  0  0 X^2 X^2  0 X^2 X^3+X^2 X^2 X^3 X^2  0 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3+X^2  0 X^2 X^2 X^3  0 X^3 X^3+X^2 X^3  0  0  0  0 X^2 X^3+X^2  0  0 X^3  0 X^3  0  0 X^3 X^2 X^3+X^2 X^3 X^3  0 X^3+X^2 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+481x^56+808x^57+2060x^58+1784x^59+2582x^60+1896x^61+2114x^62+1600x^63+1340x^64+680x^65+680x^66+136x^67+151x^68+8x^69+42x^70+16x^72+3x^76+2x^80

The gray image is a linear code over GF(2) with n=488, k=14 and d=224.
This code was found by Heurico 1.16 in 18.4 seconds.