The generator matrix

 1  0  1  1  1  2  X  1  1  1  1  0  1  1  1 X+2  X  1  1  X  1  1  X  1  1  2  1  1  1  2  1  1
 0  1  1 X+2 X+3  1  1  2  3  X X+1  1  3 X+1 X+3  1  1 X+1 X+2  1  3  3  1  2 X+2  1  1  3  X  1 X+2  2
 0  0  X  0 X+2  X X+2  X  2 X+2  0  0  2  2  X  0  X  X  0 X+2  2 X+2  0  X  X X+2  X X+2  X  2  2  X
 0  0  0  2  0  2  0  0  2  2  0  2  2  0  2  2  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0
 0  0  0  0  2  2  0  2  0  0  2  0  2  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  2  2  2  0

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+106x^28+64x^29+184x^30+64x^31+215x^32+64x^33+156x^34+64x^35+84x^36+8x^38+8x^40+4x^42+2x^44

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 0.0346 seconds.