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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  X X^2 X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2 X^2+X  0 X^3+X X^3+X^2 X^3 X^3+X X^2 X^2+X  0 X^2+X X^3+X^2  X X^3 X^3+X^2+X X^2  X  0 X^3 X^2+X X^3+X^2+X X^2 X^3+X X^2 X^3+X X^3+X^2 X^3+X^2 X^3+X  X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X  X  X X^2+X  0 X^3  0 X^3 X^2+X X^3+X^2 X^3+X^2  0
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3  0  0 X^3  0  0  0 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0
 0  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 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
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 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+48x^56+282x^57+38x^58+16x^59+40x^60+1102x^61+40x^62+208x^63+39x^64+182x^65+49x^66+2x^69+1x^114

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 0.281 seconds.