The generator matrix

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

generates a code of length 34 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+88x^25+176x^26+242x^27+308x^28+470x^29+686x^30+910x^31+1533x^32+2348x^33+2760x^34+2392x^35+1624x^36+984x^37+620x^38+480x^39+325x^40+188x^41+104x^42+70x^43+44x^44+18x^45+6x^46+2x^47+4x^48+1x^56

The gray image is a code over GF(2) with n=136, k=14 and d=50.
This code was found by Heurico 1.16 in 9.69 seconds.