The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+40x^57+6x^58+8x^59+6x^60+2x^62+1x^64

The gray image is a code over GF(2) with n=228, k=6 and d=114.
This code was found by Heurico 1.13 in 0.063 seconds.