The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  X  X  1  X  1  1  1  1  1  X  X  X  X  1 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2  X  X  X  X  1  1  1  1  X  X  X  X  X
 0 2X  0  0  0 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X 2X  0  0 2X  0 2X 2X  0  0  0 2X 2X 2X 2X  0 2X 2X 2X 2X  0  0  0  0  0  0  0 2X 2X 2X 2X  0  0  0 2X  0
 0  0 2X  0 2X 2X 2X  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0  0 2X 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X  0
 0  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0 2X 2X  0 2X 2X  0  0  0 2X 2X  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+36x^58+64x^59+12x^60+8x^62+1x^64+4x^66+2x^72

The gray image is a code over GF(2) with n=472, k=7 and d=232.
This code was found by Heurico 1.16 in 0.11 seconds.