The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+50x^73+17x^74+96x^75+22x^76+8x^77+8x^78+7x^80+36x^81+6x^82+2x^84+1x^90+2x^105

The gray image is a code over GF(2) with n=304, k=8 and d=146.
This code was found by Heurico 1.16 in 1.09 seconds.