The generator matrix

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

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+385x^54+1122x^55+1554x^56+2128x^57+2198x^58+2300x^59+2040x^60+1798x^61+1146x^62+830x^63+493x^64+184x^65+100x^66+68x^67+13x^68+18x^69+1x^70+2x^72+2x^74+1x^76

The gray image is a linear code over GF(2) with n=472, k=14 and d=216.
This code was found by Heurico 1.16 in 3.31 seconds.