The generator matrix

 1  0  0  1  1  1  0  1  2  1  1 X+2  1  X  1  1  1  2 X+2  1  1  1  X  1  1  1 X+2  1  1  1  X  X
 0  1  0  0  1  3  1  X  1 X+1 X+3  0  2  1  1  2  1  1  1 X+1  3  X  1  1  1 X+3  1  X X+3 X+2  0  0
 0  0  1 X+1 X+3  0 X+1  1  X  2  3  1 X+2  3  X  1  1  3  2 X+3  X X+3 X+1 X+1  0 X+1 X+1  3  3  0  1  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  2  2  0  2  0  0  2  2  2  2  0
 0  0  0  0  2  2  2  0  2  0  0  2  2  0  0  0  2  2  2  0  0  2  2  0  0  2  2  0  2  0  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+239x^28+116x^29+382x^30+164x^31+417x^32+120x^33+230x^34+88x^35+184x^36+20x^37+58x^38+4x^39+22x^40+2x^42+1x^44

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 0.0855 seconds.