The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1  2  1  1  X  X  1  1  0  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  1  1  1  X  1  1  1  1  1  1  1  1 X+2  1  1 X+2  1  0  1  1
 0  1  1 X+2 X+1  1  3  2  1  2  1  1  X X+3  1  1  0 X+2  1 X+3 X+2  1  1  1 X+3 X+3 X+1  3 X+1  3 X+1  3  2  0  X  0  X  0 X+2  X  0  2  0 X+2  2 X+2  0  X  X  1  0  2  1  X  1 X+2 X+1
 0  0  X  0  2  0  2  X  X X+2 X+2 X+2  X  X  0  X  0 X+2  0  2  0 X+2  2 X+2 X+2  X  0  2 X+2  X  2  0  0 X+2 X+2  X  X  2  2  0  2  0  X  2 X+2  X  2 X+2  0  0  X  X  2  2 X+2  0 X+2
 0  0  0  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  2  2  0  2  0  0  2  0  0  2  0  2  0  2  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  0  0  0  2  0  2  0  2  0  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+80x^54+84x^55+100x^56+48x^57+68x^58+40x^59+47x^60+16x^61+18x^62+4x^63+2x^68+2x^70+1x^76+1x^88

The gray image is a code over GF(2) with n=228, k=9 and d=108.
This code was found by Heurico 1.16 in 0.104 seconds.