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.