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  2  1  1  1  1  1 2X+2  1  1  1  1  1  X  1  1  X  X  X 2X+2  1  1  1  0  1  1  X  1  X  X  1  X
 0  X  0  X  0 2X 3X  X  2 X+2  2 X+2  2 3X+2 2X+2 X+2  2 3X+2 2X X+2 3X 3X+2  X  0 2X+2 3X X+2  2  X 2X 2X 2X 3X  X 2X  2 3X 2X+2 X+2  0 X+2 X+2 2X+2 2X 3X 2X  X 3X+2 3X+2  0  0 3X+2  0  X 3X  X  X X+2  2
 0  0  X  X 2X+2 3X+2 X+2  2  2 3X+2  X  0 2X 3X X+2 2X+2  X  0 X+2  2 3X  X 3X  0 2X  0 X+2 3X+2 2X+2 2X 3X+2  2  X 2X  X 3X 3X+2  2 3X 3X 3X+2 2X  X  X X+2  X  2 3X+2  X 3X+2  X 3X+2 2X+2 2X 3X 3X+2 2X+2  2  X
 0  0  0 2X  0  0  0 2X 2X  0 2X  0 2X 2X 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0 2X  0  0  0  0 2X 2X 2X  0  0 2X 2X 2X 2X  0  0 2X  0 2X 2X  0 2X 2X
 0  0  0  0 2X 2X  0  0 2X 2X 2X 2X  0 2X  0 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X 2X  0 2X  0  0 2X  0  0  0 2X  0 2X  0  0  0 2X 2X 2X  0 2X

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+160x^54+232x^55+418x^56+350x^57+648x^58+696x^59+578x^60+336x^61+293x^62+104x^63+127x^64+30x^65+42x^66+40x^67+27x^68+4x^69+9x^70+1x^92

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 0.422 seconds.