The generator matrix

 1  0  0  0  1  1  1  2  1  1  1  1  X  X  X  0  1  1  2  1  2  1  0 X+2  1  0  1  X  0  0  1  X  1  0  1  1
 0  1  0  0  0  1  3  1  2 X+2  3 X+3  1  2  1  0  0  X  1  1 X+2  3 X+2  1  3  1  X  1  X  1 X+1  1 X+2  1  3  0
 0  0  1  0  1  1  2  3 X+2  3 X+3  X  X  1 X+3  1 X+2  X  1 X+2  1  3  1  1  X X+2  3  3  X X+1  2  0  2  3  X  X
 0  0  0  1  1  2  1  1  3 X+2 X+3  0 X+3  1  2 X+2  2  3  2  3  1  0 X+2 X+1  2 X+3  1  X  1 X+3 X+1  3  X X+2  2  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  2  2 X+2 X+2 X+2 X+2  X  X  X  2 X+2  2 X+2  2  X X+2  2  X  2  0  X  X  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+84x^29+373x^30+720x^31+1005x^32+1326x^33+1643x^34+1948x^35+2039x^36+2054x^37+1869x^38+1332x^39+935x^40+554x^41+273x^42+148x^43+45x^44+14x^45+2x^46+12x^47+7x^48

The gray image is a code over GF(2) with n=144, k=14 and d=58.
This code was found by Heurico 1.13 in 2.04 seconds.