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

generates a code of length 58 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+13x^54+24x^55+20x^56+104x^57+707x^58+104x^59+8x^60+24x^61+15x^62+3x^64+1x^114

The gray image is a code over GF(2) with n=464, k=10 and d=216.
This code was found by Heurico 1.16 in 0.171 seconds.