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  X  0 X^2  X  0 X^2  1
 0  X X^3+X^2 X^2+X  0 X^2+X X^3+X^2 X^3+X X^2+X  0 X^3+X X^3+X^2 X^3+X  0 X^3+X^2+X X^3+X^2 X^2+X  0 X^3+X X^3+X^2 X^3 X^2+X X^2 X^3+X  0 X^3+X^2+X X^3+X^2 X^3+X X^3 X^2+X X^2  X  0 X^3 X^2+X X^3+X^2+X X^2  X X^2  X X^3+X^2 X^3+X^2 X^3+X X^3+X X^3+X^2 X^3+X^2 X^2 X^2 X^3+X X^3+X  X  X X^2+X  X X^3+X^2 X^3+X  X X^3+X^2  0
 0  0 X^3  0  0  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  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  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0  0 X^3  0
 0  0  0 X^3  0  0  0  0  0  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 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0
 0  0  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0 X^3 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0  0
 0  0  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0  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+38x^54+200x^55+110x^56+162x^57+239x^58+562x^59+238x^60+156x^61+98x^62+196x^63+33x^64+2x^65+8x^66+2x^67+2x^68+1x^106

The gray image is a linear code over GF(2) with n=472, k=11 and d=216.
This code was found by Heurico 1.16 in 0.25 seconds.