The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^70+644x^71+1293x^72+1670x^73+1689x^74+2142x^75+2118x^76+1918x^77+1441x^78+1254x^79+757x^80+610x^81+369x^82+154x^83+101x^84+38x^85+29x^86+12x^87+7x^88+4x^89+2x^90+3x^92+2x^95

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 3.53 seconds.