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

generates a code of length 59 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+142x^54+46x^56+192x^57+362x^58+640x^59+256x^60+192x^61+130x^62+16x^64+70x^66+1x^112

The gray image is a code over GF(2) with n=472, k=11 and d=216.
This code was found by Heurico 1.16 in 18 seconds.