The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  X  X  0  1  1  0  X  X  X
 0  X  0  X  0  0  X X+2  2  2  X X+2 X+2 X+2  2  2  0  X  X  2  2  0  0 X+2 X+2  0 X+2 X+2  X X+2  2  2
 0  0  X  X  0 X+2  X  2  0  X  X  0  2  X  2 X+2  0 X+2  X  0  X X+2  X  2  0  X  2  2  0  0  X X+2
 0  0  0  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  2  0  0  0  0  2  2  0
 0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  2  2  2  2  2  2  0  2
 0  0  0  0  0  2  2  2  2  2  0  0  0  0  0  2  2  2  2  2  0  2  0  2  0  2  2  0  2  2  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+218x^28+128x^30+352x^32+128x^34+172x^36+22x^40+2x^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 2.81 seconds.