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  X  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1 X^2  X  1 X^2  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0 X^3 X^3  0 X^2 X^2 X^3+X^2 X^3+X^2  0 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2 X^2  0 X^2 X^3+X^2 X^3 X^3 X^2 X^3 X^2 X^2 X^2  0  0 X^3+X^2 X^3 X^2 X^3 X^3+X^2  0  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2 X^3  0  0  0 X^3 X^2 X^2 X^3 X^2  0 X^3+X^2 X^3 X^2
 0  0 X^3+X^2  0 X^2 X^2 X^2 X^3 X^3+X^2 X^3  0 X^2 X^2 X^2  0  0  0 X^3 X^3+X^2 X^3+X^2 X^2 X^2  0 X^3 X^2  0 X^3+X^2  0 X^3+X^2 X^3 X^3 X^3+X^2  0 X^2 X^3 X^3+X^2 X^2 X^3  0 X^3+X^2 X^3 X^3  0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2  0 X^2 X^3+X^2 X^3+X^2 X^2  0  0 X^3+X^2 X^2 X^2 X^3 X^3+X^2  0
 0  0  0 X^3+X^2 X^2 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^2  0 X^3+X^2 X^2 X^3  0 X^3+X^2 X^2 X^2 X^3  0 X^3+X^2 X^3 X^3+X^2 X^3+X^2  0 X^3  0 X^3 X^2 X^2 X^3 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3 X^3 X^2 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^3+X^2 X^2 X^3  0 X^3 X^3  0 X^3 X^3+X^2 X^3 X^2 X^2 X^2 X^3
 0  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  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+160x^56+64x^58+96x^59+596x^60+320x^61+448x^62+96x^63+188x^64+68x^68+10x^72+1x^112

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 0.469 seconds.