The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+680x^56+552x^57+948x^58+432x^59+563x^60+176x^61+304x^62+176x^63+145x^64+8x^65+84x^66+25x^68+2x^76

The gray image is a code over GF(2) with n=472, k=12 and d=224.
This code was found by Heurico 1.16 in 102 seconds.