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

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+171x^54+246x^55+427x^56+462x^57+541x^58+562x^59+549x^60+438x^61+274x^62+142x^63+101x^64+54x^65+93x^66+10x^67+9x^68+6x^69+9x^70+1x^88

The gray image is a code over GF(2) with n=472, k=12 and d=216.
This code was found by Heurico 1.16 in 0.437 seconds.