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  X  1  1  1  1 X^3  1  1  1  1  1  1  X  1  X  0  X  1  X  0  1
 0  X  0 X^2+X X^2 X^3+X^2+X X^3+X^2  X X^2 X^2+X  0 X^2+X X^3 X^3+X X^2  X  0 X^2+X X^2  X X^3+X^2+X X^3+X^2 X^3+X X^3 X^2+X  0 X^2  X X^3+X X^3+X^2 X^3+X^2  X X^3+X^2+X X^2 X^2+X X^3 X^3+X X^3 X^3+X^2+X  X  0 X^2+X X^2  X X^3+X^2+X X^2+X X^2+X  X X^3+X X^3+X X^2+X  X  X  X X^2+X X^3+X^2+X X^3+X  X  0
 0  0 X^3+X^2  0 X^2 X^2 X^3 X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^3 X^3  0 X^3 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^2  0 X^3 X^2 X^3+X^2  0 X^2  0 X^3+X^2  0  0 X^3+X^2  0 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3+X^2 X^2 X^3 X^3 X^2 X^2 X^2  0 X^3 X^3 X^3+X^2 X^3  0 X^2  0  0  0
 0  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0  0
 0  0  0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0 X^3  0 X^3 X^3  0 X^3  0 X^3  0 X^3  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+61x^54+86x^55+205x^56+164x^57+316x^58+412x^59+310x^60+150x^61+192x^62+74x^63+56x^64+4x^65+5x^66+4x^67+4x^68+2x^69+1x^74+1x^102

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 0.313 seconds.