The generator matrix

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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+16x^60+8x^61+5x^62+1x^64+1x^66

The gray image is a linear code over GF(2) with n=472, k=5 and d=240.
This code was found by Heurico 1.16 in 0.094 seconds.