The generator matrix

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

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+338x^26+536x^27+1170x^28+1196x^29+1912x^30+1800x^31+2316x^32+1912x^33+2096x^34+1288x^35+1040x^36+380x^37+288x^38+56x^39+42x^40+6x^42+6x^44+1x^48

The gray image is a code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.13 in 5.36 seconds.