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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+91x^54+554x^55+632x^56+720x^57+562x^58+586x^59+312x^60+282x^61+96x^62+104x^63+61x^64+46x^65+33x^66+12x^67+2x^68+1x^70+1x^74

The gray image is a code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 0.188 seconds.