The generator matrix

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

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+184x^27+256x^28+506x^29+330x^30+602x^31+413x^32+638x^33+276x^34+428x^35+212x^36+160x^37+34x^38+34x^39+14x^40+6x^41+2x^45

The gray image is a code over GF(2) with n=128, k=12 and d=54.
This code was found by Heurico 1.16 in 0.303 seconds.