The generator matrix

 1  0  1  1  1  2  1  1  X  X  1  1  2  1  1 X+2  1  1  0  1  1  X  1  1 X+2 X+2 X+2 X+2  2  0 X+2  0  X  0 X+2  0 X+2  X  1  1 X+2  1  1  0  1  2  1  1  1  X  1  1  1 X+2  0  1  1
 0  1  1  0 X+1  1 X+3  0  1  1  2  1  1  X X+1  1 X+2 X+1  1  X  1  1  X  3  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0 X+3  1 X+3  2  1  0  1  1 X+3  3 X+2 X+3  X  2  1  X  3 X+2
 0  0  X  0  0  0  0  X X+2 X+2  X  X  2 X+2 X+2 X+2 X+2 X+2  2  2  2 X+2  2  2  X  0  2  2  X X+2  2  X  0 X+2  0  X  2  0  2  X X+2  0  X  X  X  0  2 X+2 X+2  2  2  0 X+2  X X+2 X+2  0
 0  0  0  X  2 X+2 X+2  X  2 X+2  2 X+2 X+2  0  X  X X+2  2  2 X+2  X  0  2  0  X  0  X X+2  0  0  0  X  2  2  X X+2  2 X+2  2  0 X+2  X X+2  2  0  2  2 X+2  X X+2 X+2  2  0  0  X X+2 X+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+202x^53+84x^54+120x^55+60x^56+148x^57+48x^58+136x^59+28x^60+118x^61+24x^62+32x^63+6x^64+10x^65+3x^66+2x^73+1x^80+1x^82

The gray image is a code over GF(2) with n=228, k=10 and d=106.
This code was found by Heurico 1.16 in 28.7 seconds.