The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+6x^58+100x^59+6x^60+2x^62+12x^63+1x^64

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 0.172 seconds.