The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+136x^26+40x^27+505x^28+308x^29+1219x^30+952x^31+1937x^32+1796x^33+2668x^34+1720x^35+1956x^36+956x^37+1156x^38+360x^39+502x^40+12x^41+132x^42+27x^44+1x^62

The gray image is a code over GF(2) with n=136, k=14 and d=52.
This code was found by Heurico 1.16 in 5.77 seconds.