The generator matrix

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

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 29.

Homogenous weight enumerator: w(x)=1x^0+32x^29+70x^30+60x^31+150x^32+136x^33+170x^34+284x^35+230x^36+280x^37+238x^38+148x^39+117x^40+56x^41+14x^42+20x^43+2x^44+8x^45+20x^46+11x^48+1x^56

The gray image is a code over GF(2) with n=144, k=11 and d=58.
This code was found by Heurico 1.16 in 31.9 seconds.