The generator matrix

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

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+46x^26+114x^27+309x^28+602x^29+820x^30+1190x^31+1797x^32+2242x^33+2269x^34+2034x^35+1756x^36+1390x^37+892x^38+482x^39+224x^40+118x^41+60x^42+20x^43+5x^44+8x^46+2x^48+1x^50+2x^52

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 4.81 seconds.