The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+88x^26+342x^27+483x^28+822x^29+823x^30+1018x^31+1040x^32+1052x^33+907x^34+796x^35+361x^36+262x^37+117x^38+50x^39+15x^40+8x^41+1x^42+2x^43+4x^44

The gray image is a code over GF(2) with n=128, k=13 and d=52.
This code was found by Heurico 1.13 in 0.468 seconds.