The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^3+X^2  1  1 X^3+X  1  1  0  1  1 X^2+X  1  1 X^3+X X^3+X^2  1  1  0 X^3+X  1  1  1  1  1  1  1  1  1 X^3+X^2 X^2+X  1  1  1  1  1  1  1  0 X^3 X^2+X X^3+X^2+X  1  1  1  1 X^3 X^2  1  1  1  1 X^2+X
 0  1 X+1 X^2+X X^2+1  1 X^3+X^2+X+1 X^3+X^2  1 X^3+X X^3+1  1  0 X+1  1 X^2+X X^2+1  1 X^3+X^2 X^3+X^2+X+1  1  1 X^3+X X^3+1  1  1  0 X^2+X X^3+X^2 X^3+X X+1 X^2+1 X^3+X^2+X+1 X^3+1 X^2+X  1  1  0 X^3 X^3+X^2+X X+1 X^2+1 X^3+X+1 X^3+X^2+1  1  1  1  1 X^3+X^2 X^2 X^3+X  X  X  1 X^3+X^2+X+1 X^3+1 X^2+X+1 X^2+1  1
 0  0 X^3  0  0  0  0 X^3 X^3 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0  0  0  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3 X^3  0 X^3 X^3  0  0  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0  0  0 X^3 X^3 X^3
 0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3  0  0 X^3 X^3 X^3  0  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 X^3 X^3  0  0  0  0  0  0  0  0  0  0  0  0  0  0 X^3 X^3 X^3  0  0  0 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0 X^3 X^3  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3 X^3  0 X^3  0 X^3  0  0 X^3  0  0 X^3 X^3  0  0  0 X^3  0 X^3  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+120x^55+276x^56+216x^57+266x^58+256x^59+378x^60+160x^61+212x^62+136x^63+14x^64+8x^65+2x^66+2x^76+1x^80

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 0.156 seconds.