The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+58x^24+134x^26+264x^28+64x^29+606x^30+320x^31+1224x^32+640x^33+1585x^34+640x^35+1197x^36+320x^37+633x^38+64x^39+272x^40+104x^42+42x^44+8x^46+13x^48+1x^50+1x^52+1x^54

The gray image is a code over GF(2) with n=136, k=13 and d=48.
This code was found by Heurico 1.16 in 2.09 seconds.