The generator matrix

 1  0  1  1  1 X+2  1  1  1  0  1 X+2  1  1  1  1 X+2  1  0  1  1  1  X  1  1  0  1  1  2  2  1  1
 0  1 X+1 X+2  1  1 X+1  3  0  1 X+2  1  3 X+1  0  3  1 X+2  1 X+1 X+3  3 X+2 X+3  0  1  3  2  1  2 X+3  0
 0  0  2  0  0  0  2  0  2  2  2  2  2  0  0  2  0  0  0  0  2  2  0  2  2  2  0  0  0  2  2  0
 0  0  0  2  0  2  2  2  2  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  2  2  2  2  2  2  0  0
 0  0  0  0  2  0  2  2  0  0  0  0  2  2  0  2  0  0  0  2  2  0  2  0  2  2  0  2  2  2  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+23x^28+54x^29+105x^30+60x^31+86x^32+24x^33+63x^34+36x^35+31x^36+18x^37+7x^38+1x^40+1x^42+2x^44

The gray image is a code over GF(2) with n=128, k=9 and d=56.
This code was found by Heurico 1.16 in 0.0147 seconds.