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

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

Homogenous weight enumerator: w(x)=1x^0+108x^70+164x^71+381x^72+210x^73+543x^74+286x^75+799x^76+270x^77+499x^78+210x^79+364x^80+116x^81+89x^82+4x^83+16x^84+6x^85+8x^86+6x^87+6x^88+6x^89+2x^91+1x^102+1x^116

The gray image is a code over GF(2) with n=608, k=12 and d=280.
This code was found by Heurico 1.16 in 0.984 seconds.