The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 27.

Homogenous weight enumerator: w(x)=1x^0+132x^27+294x^28+464x^29+428x^30+614x^31+393x^32+524x^33+402x^34+392x^35+210x^36+144x^37+48x^38+30x^39+14x^40+4x^41+2x^42

The gray image is a code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.11 in 0.128 seconds.