The generator matrix

 1  0  0  1  1  1  0  1  1  X  0  1  X  1  1  2  1  1  X X+2  1  1  1  1  0  1  2  X  1 X+2 X+2  1 X+2  X  0  1
 0  1  0  1  X X+3  1  0 X+3  1  1  2  X  1  1  1 X+1 X+2  2  1 X+2  3 X+2 X+2  1 X+1  2  1  X  X  1  2  1 X+2  1  0
 0  0  1  1  1  0 X+3  X  X  1 X+2 X+1  1  1  X  X X+1 X+1  1 X+3  X X+2  2 X+1  2 X+1  1  X  X  1  0  2 X+3  1 X+3  0
 0  0  0  X  0 X+2 X+2  X  2  2  X  X  2  0  0  2  0  2 X+2  2  X X+2  0 X+2 X+2  2  0  X  0  X  X  0  X X+2 X+2  0
 0  0  0  0  2  0  0  2  2  2  2  0  0  2  0  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  2  0  2  2  2  0
 0  0  0  0  0  2  0  0  0  2  2  0  2  0  2  2  2  2  2  0  2  2  2  0  0  0  0  2  0  0  0  0  2  0  0  2
 0  0  0  0  0  0  2  2  0  2  0  2  2  2  0  0  0  2  0  0  2  2  0  0  0  0  2  2  2  2  0  2  2  0  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+37x^28+158x^29+312x^30+590x^31+892x^32+1492x^33+1378x^34+2420x^35+1922x^36+2320x^37+1438x^38+1456x^39+816x^40+620x^41+318x^42+140x^43+41x^44+18x^45+10x^46+2x^47+2x^48+1x^64

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 5.44 seconds.