The generator matrix

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

generates a code of length 59 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+206x^56+288x^57+236x^58+30x^60+40x^62+81x^64+96x^65+40x^66+2x^68+4x^74

The gray image is a code over GF(2) with n=236, k=10 and d=112.
This code was found by Heurico 1.16 in 64.3 seconds.