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  1  1  1  1  1  1  1  1  1
 0 X^3  0  0  0  0  0  0  0  0  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 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  0 X^3 X^3
 0  0 X^3  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3
 0  0  0 X^3  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  0
 0  0  0  0 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  0  0 X^3  0  0 X^3  0 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0 X^3  0  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 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0  0  0  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+15x^54+16x^56+32x^58+896x^59+32x^60+16x^62+15x^64+1x^118

The gray image is a linear code over GF(2) with n=472, k=10 and d=216.
This code was found by Heurico 1.16 in 0.141 seconds.