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

generates a code of length 55 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+72x^51+626x^52+488x^53+756x^54+664x^55+577x^56+272x^57+209x^58+144x^59+195x^60+24x^61+58x^62+8x^64+1x^66+1x^76

The gray image is a code over GF(2) with n=440, k=12 and d=204.
This code was found by Heurico 1.16 in 0.172 seconds.