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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+38x^54+200x^55+110x^56+162x^57+239x^58+562x^59+238x^60+156x^61+98x^62+196x^63+33x^64+2x^65+8x^66+2x^67+2x^68+1x^106

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 0.234 seconds.