The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+36x^29+76x^30+104x^31+130x^32+140x^33+142x^34+112x^35+88x^36+68x^37+40x^38+32x^39+17x^40+12x^41+14x^42+8x^43+3x^44+1x^52

The gray image is a code over GF(2) with n=136, k=10 and d=58.
This code was found by Heurico 1.16 in 0.0486 seconds.