The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+46x^56+32x^57+36x^58+7x^60+2x^62+1x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=228, k=7 and d=112.
This code was found by Heurico 1.16 in 0.0689 seconds.