The generator matrix

 1  0  1  1  1  2  1  1  0  1  1  0  X  1  1  1  1  0  1  1  1  1  2  2  X  0 X+2  0 X+2 X+2  X  X
 0  1  1  0 X+1  1  1  0  1  2 X+1  1  1  3 X+2  X X+1  1  X  X X+3  1  1  1  1  0  1  1  1  1  1  1
 0  0  X  0  0  2  0 X+2 X+2 X+2 X+2 X+2  2  2  0  2  0  2 X+2  X X+2 X+2  X X+2  0  X  2  2  0  0  X  X
 0  0  0  X  2  X X+2 X+2 X+2  2  X  2 X+2  2  0  X X+2  0  2 X+2  0  X  2 X+2  X  0  X  X X+2  0  0  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+38x^28+128x^29+216x^30+152x^31+51x^32+112x^33+152x^34+96x^35+32x^36+16x^37+12x^38+8x^39+4x^40+2x^44+4x^46

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 0.0316 seconds.