The generator matrix

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

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+140x^26+204x^27+662x^28+600x^29+986x^30+968x^31+1091x^32+1028x^33+996x^34+604x^35+502x^36+160x^37+178x^38+16x^39+48x^40+4x^41+4x^42

The gray image is a code over GF(2) with n=128, k=13 and d=52.
This code was found by Heurico 1.16 in 1.31 seconds.