The generator matrix

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

generates a code of length 31 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+67x^26+24x^27+156x^28+64x^29+186x^30+80x^31+168x^32+64x^33+102x^34+24x^35+51x^36+26x^38+7x^40+3x^42+1x^44

The gray image is a code over GF(2) with n=124, k=10 and d=52.
This code was found by Heurico 1.16 in 0.042 seconds.