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

generates a code of length 62 over Z2[X]/(X^4) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+59x^56+110x^58+80x^59+219x^60+272x^61+534x^62+368x^63+207x^64+48x^65+76x^66+45x^68+14x^70+12x^72+2x^74+1x^112

The gray image is a linear code over GF(2) with n=496, k=11 and d=224.
This code was found by Heurico 1.16 in 0.296 seconds.