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

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+43x^70+218x^71+335x^72+350x^73+491x^74+466x^75+489x^76+518x^77+338x^78+324x^79+177x^80+90x^81+98x^82+50x^83+61x^84+18x^85+4x^86+14x^87+9x^88+1x^90+1x^110

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 0.765 seconds.