The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  0  1  2  1  1  0  1  2 X+2  1  X  1  X  0  1  1  1  1  0 X+2  2  0
 0  1  0  0  3 X+1  1  0 X+3  2  1 X+1  1  2  3  1  2  1 X+2 X+2  1  X X+2  1  0 X+2  3  2  1  X  1 X+2
 0  0  1  1  3  2  3  1 X+3  0  3 X+2 X+2 X+1  0  2 X+1 X+3  1  0 X+2 X+1  1 X+2  X  3  1  X  X  1 X+1  1
 0  0  0  X  X  0  X X+2  2  X  2  X  0 X+2  2  X  0  X  0  0  0  2 X+2 X+2 X+2  X  0  X  2  2 X+2 X+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+219x^28+172x^29+288x^30+236x^31+348x^32+208x^33+218x^34+112x^35+117x^36+36x^37+68x^38+4x^39+19x^40+2x^42

The gray image is a code over GF(2) with n=128, k=11 and d=56.
This code was found by Heurico 1.16 in 0.0823 seconds.