The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+127x^28+288x^30+200x^32+288x^34+110x^36+6x^40+3x^44+1x^48

The gray image is a code over GF(2) with n=128, k=10 and d=56.
This code was found by Heurico 1.16 in 0.126 seconds.