The generator matrix

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

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+9x^56+24x^57+22x^58+144x^59+22x^60+24x^61+9x^62+1x^118

The gray image is a code over GF(2) with n=236, k=8 and d=112.
This code was found by Heurico 1.16 in 0.11 seconds.