The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+64x^54+140x^55+92x^56+32x^57+34x^58+52x^59+30x^60+8x^61+22x^62+24x^63+11x^64+1x^68+1x^76

The gray image is a code over GF(2) with n=228, k=9 and d=108.
This code was found by Heurico 1.13 in 0.047 seconds.