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 X^2  1  1  1  1  1  1  1  1  1  1  1  1  1  1
 0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^3 X^2 X^3 X^3+X^2 X^2  0 X^3 X^2 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^2  0 X^3  0  0 X^3 X^3+X^2 X^2  0  0 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^2 X^2
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 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 X^3  0  0  0 X^3 X^3 X^3  0  0
 0  0  0 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 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 X^3 X^3
 0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0  0  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0 X^3  0 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 X^3  0 X^3 X^3 X^3  0 X^3  0  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+135x^56+456x^60+1024x^61+256x^62+87x^64+88x^68+1x^120

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 3.7 seconds.