The generator matrix

 1  0  1  1  1  0  1  1  X  1  1  2  1  1  X  1  1 X+2  0  1  1  0  1  1 X+2  X  1  1  1  X  X  2  1  X  2  X
 0  1  1  0  1  1  0 X+1  1 X+2 X+1  1 X+3  2  1 X+1  0  1  1 X+1  0  1  3 X+3  1  1  0 X+1 X+1 X+2  X  1 X+2 X+2  X  0
 0  0  X  0  0  0  0  X  0  0 X+2  2 X+2  X  X  2 X+2  X X+2  2 X+2  X  X  X  2 X+2  0  X  0  2  2  2  X  0  X  X
 0  0  0  X  0  0  0  0  2 X+2 X+2 X+2  X  2 X+2  0  2  0  2 X+2  X  0 X+2  2 X+2  2  2  X  X  2  X  0  2  0  0 X+2
 0  0  0  0  X X+2 X+2  X X+2 X+2  2  0 X+2  0 X+2  0 X+2  X  2 X+2  2 X+2  0  2  X  0  2  2  0 X+2  2  2  X  X  2  0
 0  0  0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  2  0
 0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  2  0  2  0  0  2  2  0  0  2  2  0  2

generates a code of length 36 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 28.

Homogenous weight enumerator: w(x)=1x^0+177x^28+76x^29+564x^30+368x^31+1241x^32+964x^33+1960x^34+1672x^35+2358x^36+1572x^37+1980x^38+1120x^39+1250x^40+316x^41+512x^42+40x^43+152x^44+16x^45+40x^46+4x^48+1x^60

The gray image is a code over GF(2) with n=144, k=14 and d=56.
This code was found by Heurico 1.16 in 6.41 seconds.