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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+57x^70+4x^71+121x^72+36x^73+93x^74+88x^75+247x^76+88x^77+113x^78+36x^79+53x^80+4x^81+51x^82+20x^84+6x^86+5x^88+1x^140

The gray image is a code over GF(2) with n=304, k=10 and d=140.
This code was found by Heurico 1.16 in 0.374 seconds.