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

generates a code of length 59 over Z2[X]/(X^4) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+108x^55+87x^56+108x^57+832x^58+88x^59+551x^60+56x^61+16x^62+60x^63+48x^64+92x^65+1x^116

The gray image is a linear code over GF(2) with n=472, k=11 and d=220.
This code was found by Heurico 1.16 in 9.05 seconds.