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  X  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  X  X  1  1  X  1  X  1
 0 X^3  0  0  0  0  0  0  0  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3  0
 0  0 X^3  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3  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 X^3 X^3  0
 0  0  0 X^3  0  0  0  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0  0  0  0  0
 0  0  0  0 X^3  0  0  0  0  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  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  0  0 X^3  0 X^3  0 X^3 X^3  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 X^3  0  0  0 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3
 0  0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0  0 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0
 0  0  0  0  0  0  0 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0 X^3  0 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+117x^56+144x^60+1536x^62+178x^64+16x^68+55x^72+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 3.2 seconds.