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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+68x^53+27x^54+54x^56+140x^57+176x^58+1152x^59+176x^60+116x^61+50x^62+24x^64+36x^65+24x^69+3x^70+1x^112

The gray image is a linear code over GF(2) with n=472, k=11 and d=212.
This code was found by Heurico 1.16 in 5.28 seconds.