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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+24x^69+30x^70+52x^71+85x^72+30x^73+138x^74+8x^75+144x^76+274x^77+82x^78+36x^79+25x^80+34x^81+6x^82+16x^83+22x^85+16x^87+1x^136

The gray image is a code over GF(2) with n=304, k=10 and d=138.
This code was found by Heurico 1.16 in 3.93 seconds.