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

generates a code of length 61 over Z2[X]/(X^4) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+46x^58+24x^59+153x^60+592x^61+132x^62+24x^63+45x^64+6x^66+1x^116

The gray image is a linear code over GF(2) with n=488, k=10 and d=232.
This code was found by Heurico 1.16 in 5.09 seconds.