The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+70x^56+122x^58+640x^59+128x^60+52x^62+8x^64+2x^66+1x^112

The gray image is a linear code over GF(2) with n=472, k=10 and d=224.
This code was found by Heurico 1.16 in 28.3 seconds.