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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+19x^72+100x^73+34x^74+108x^75+29x^76+80x^77+26x^78+80x^79+12x^80+12x^81+1x^82+4x^83+1x^84+2x^86+2x^92+1x^130

The gray image is a code over GF(2) with n=304, k=9 and d=144.
This code was found by Heurico 1.16 in 0.225 seconds.