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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+244x^71+351x^72+328x^73+341x^74+404x^75+819x^76+388x^77+339x^78+324x^79+292x^80+204x^81+19x^82+16x^83+8x^85+5x^86+4x^87+8x^88+1x^132

The gray image is a code over GF(2) with n=608, k=12 and d=284.
This code was found by Heurico 1.16 in 55.8 seconds.