The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+304x^69+1548x^70+2778x^71+4090x^72+6096x^73+6797x^74+7536x^75+7965x^76+7514x^77+6875x^78+5578x^79+3707x^80+2258x^81+1328x^82+648x^83+282x^84+150x^85+31x^86+16x^87+10x^88+14x^89+5x^90+4x^91+1x^92

The gray image is a code over GF(2) with n=608, k=16 and d=276.
This code was found by Heurico 1.16 in 41.2 seconds.