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

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

Homogenous weight enumerator: w(x)=1x^0+132x^54+127x^56+192x^57+290x^58+640x^59+224x^60+192x^61+158x^62+29x^64+46x^66+14x^70+2x^72+1x^104

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 38.1 seconds.