The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+51x^50+172x^51+179x^52+400x^53+299x^54+494x^55+260x^56+502x^57+305x^58+462x^59+213x^60+358x^61+127x^62+106x^63+62x^64+38x^65+12x^66+14x^67+14x^68+10x^69+6x^70+5x^72+4x^73+2x^76

The gray image is a code over GF(2) with n=228, k=12 and d=100.
This code was found by Heurico 1.16 in 0.791 seconds.