The generator matrix

 1  0  0  1  1  1  0  1  1  X X+2  0  1  1 X+2  1  1  2  1  2  1  X  1  1  1  1  1  2  2  2 X+2  0  1  1
 0  1  0  1  X X+3  1  0 X+3  1  X  1  2 X+1  1  X  1  1  X  X  3  1  3 X+3  2 X+3  1  1  0  X  2  1 X+3  0
 0  0  1  1  1  0 X+3  X  X  1  1  X  1 X+1  X  0 X+1 X+3  3  1  3 X+3  0  2 X+3  1 X+2  1  1  2  1  X X+1  0
 0  0  0  X  0 X+2 X+2  X  2  2 X+2 X+2  0  0 X+2 X+2 X+2  0 X+2  X  0  X  X  2  X  2  X X+2 X+2 X+2  2 X+2 X+2  0
 0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  0  0  2  0  2  0  2  2  0  2  0  0  0  0  0  2  0  0  0
 0  0  0  0  0  2  0  0  0  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  2  0  2  0  2  2  2  0
 0  0  0  0  0  0  2  2  0  2  2  2  2  0  0  0  2  0  0  0  2  2  0  0  2  2  2  0  2  2  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+43x^26+142x^27+398x^28+606x^29+968x^30+1296x^31+1566x^32+2062x^33+2121x^34+2044x^35+1809x^36+1306x^37+897x^38+592x^39+307x^40+122x^41+63x^42+22x^43+13x^44+3x^46+2x^48+1x^58

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 4.9 seconds.