The generator matrix

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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+232x^55+539x^56+274x^57+161x^58+174x^59+382x^60+158x^61+37x^62+42x^63+29x^64+16x^65+1x^70+1x^74+1x^80

The gray image is a code over GF(2) with n=464, k=11 and d=220.
This code was found by Heurico 1.16 in 0.14 seconds.