The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+116x^53+77x^54+244x^55+76x^56+200x^57+37x^58+76x^59+25x^60+56x^61+24x^62+44x^63+9x^64+20x^65+5x^66+1x^68+8x^69+1x^70+4x^71

The gray image is a code over GF(2) with n=228, k=10 and d=106.
This code was found by Heurico 1.11 in 0.0852 seconds.