The generator matrix

 1  0  1  1  1  0  1 X+2  1  1 X+2  1  1  1  1  X  1  2 X+2  1  1  X  X  X  1  1  1  1  2  1  1  X
 0  1  1  0 X+3  1  X  1 X+3  X  1 X+1  0  1 X+2  1 X+3  1  1 X+2  2  1  1  1  0  0 X+1  2  1  0 X+3  1
 0  0  X  0 X+2  X  0  X  0  X  2  2  X X+2  X X+2 X+2  X  2  0 X+2  0  2 X+2  2  X  0  X  2  0  0  X
 0  0  0  X  0  X  X  X X+2  0  2  2 X+2  X  X  2  X  2 X+2  0  2  X  0 X+2 X+2  2  0 X+2 X+2  2  X  2
 0  0  0  0  2  2  2  0  2  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2  2  2  2  2  0  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+332x^28+384x^30+648x^32+384x^34+264x^36+30x^40+4x^44+1x^48

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 21.7 seconds.