The generator matrix

 1  0  0  0  1  1  1  1  2  1  1  1  X X+2  0  1  1 X+2  0  1  2  1  1 X+2  2  X  1  0  0  X  1  1
 0  1  0  0  0  0  1  3  1  2 X+1  3  1  1  X  X  3  1 X+2  1  2 X+3 X+3  1  1  X  0  1  2  0  X X+2
 0  0  1  0  0  1  1  2  3  3 X+1 X+2  X X+3  1  2  1  2  1 X+3  1  2  2  X  3  X X+1 X+1  1  X  X  0
 0  0  0  1 X+1 X+3  2 X+3 X+3  X X+1 X+2  3  2  3  2  X X+1  X X+1 X+3 X+1  1  2  3  1  X X+3  2  1  0  1
 0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  0  2  2  2  0  2  2  2  2  0  2
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  2  2  0  2  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+389x^26+512x^27+1116x^28+1092x^29+1875x^30+1964x^31+2448x^32+2048x^33+1909x^34+1096x^35+1125x^36+372x^37+297x^38+76x^39+43x^40+8x^41+10x^42+3x^44

The gray image is a code over GF(2) with n=128, k=14 and d=52.
This code was found by Heurico 1.16 in 89.4 seconds.