The generator matrix

 1  0  0  1  1  1 2X+2 2X  0  2  1  1  1  1 3X  1  1 3X+2  1  1 3X  1 3X+2 3X+2  1 3X  1  1  1  1  2  1  1 2X  0  0  1  1 3X X+2 X+2 3X+2  1  2 X+2  0  1 X+2  1  1 3X+2  1  1 2X  1  1 3X  1  1 3X  1  1 2X+2  1  1 2X  1 3X 2X+2  1  1  1  0  1 X+2  1
 0  1  0  0  3 2X+3  1 X+2  1  1 2X  0  3  3 3X X+2 X+3  1 X+1  X  1  X  1  2 3X+1  1 X+3 3X+2 2X 2X+1  1 3X+1 2X  1  2  1 3X+3 3X+1 3X+2  1  1  1  X  1 2X+2  X 2X+3  1 2X  1  1 2X+1 2X+2  1 3X X+1  1 3X  3  1 3X+1 3X+1  1 X+3  3  1 X+2 2X+2  1 3X+2 3X+3 X+2  1 2X+2 X+2  0
 0  0  1 X+1 X+3  2 X+3  1 3X+2  1 X+2  3 2X+1  X  1  3  1 3X+2 3X X+2 X+3  2 2X+2  1 X+3 2X+3  0 3X+1  3  2 3X+3 2X+1 X+2 2X  1 2X+1 2X+2 3X+3  1 3X+3  X 2X+2 2X+1 X+2  1  1 3X  X 3X+1  1 2X+3 3X 3X+1  0 X+2  2  1  0 X+3 2X 2X 3X+3 X+1 X+2 2X 3X+1 2X+1  1  1 X+1  3 X+3 X+2  2  1  0
 0  0  0  2  2  0  2 2X+2  2 2X 2X+2 2X 2X 2X+2  0  0  0 2X  2  2  0 2X  0  2 2X+2  2  2 2X  2  2 2X  2  0  2  2 2X+2 2X  2  2  2  0  2 2X+2  0 2X+2 2X  2 2X+2 2X 2X+2 2X 2X  0 2X 2X 2X 2X  0  0 2X 2X+2  0  0 2X 2X+2 2X+2 2X+2  0  0  0 2X+2 2X+2 2X 2X+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+90x^70+714x^71+1271x^72+1684x^73+1767x^74+2118x^75+1970x^76+1730x^77+1610x^78+1362x^79+831x^80+586x^81+285x^82+186x^83+81x^84+42x^85+22x^86+20x^87+3x^88+4x^89+2x^90+3x^92+2x^97

The gray image is a code over GF(2) with n=608, k=14 and d=280.
This code was found by Heurico 1.16 in 3.7 seconds.