The generator matrix

 1  0  0  1  1  1  2  0  0  1  1  1  1  X  2  1  1  1  2  1  1  X  1  1  X  1  0  X  1  1  1  1
 0  1  0  0  1  1  1  0  1  2  3 X+1  X  1  1 X+2  3 X+1  1 X+1  X  0 X+3 X+2 X+2 X+3  1  1 X+3 X+3  3 X+2
 0  0  1  1  2  3  1  1  1  0  1 X+2 X+3  2 X+2  3  X  1 X+1  2  2  1  X  3  1  2 X+2  3  0  3  0  X
 0  0  0  X  0  X  X X+2  2  X  2  X  X  X  2  0  0 X+2 X+2  X X+2  0  0  2  X  2  X X+2 X+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+255x^28+112x^29+334x^30+164x^31+422x^32+144x^33+286x^34+56x^35+165x^36+32x^37+50x^38+4x^39+21x^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 1.11 in 0.06 seconds.