The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+309x^72+148x^76+49x^80+4x^84+1x^136

The gray image is a code over GF(2) with n=296, k=9 and d=144.
This code was found by Heurico 1.16 in 22.5 seconds.