The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+88x^55+616x^56+644x^57+704x^58+582x^59+455x^60+252x^61+305x^62+194x^63+116x^64+36x^65+61x^66+24x^67+12x^68+4x^71+2x^74

The gray image is a code over GF(2) with n=472, k=12 and d=220.
This code was found by Heurico 1.16 in 0.187 seconds.