The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+176x^67+1151x^68+2852x^69+5795x^70+9348x^71+15285x^72+20066x^73+27024x^74+31780x^75+34602x^76+31272x^77+29156x^78+20480x^79+14786x^80+9000x^81+4831x^82+2480x^83+1215x^84+456x^85+259x^86+62x^87+30x^88+14x^89+7x^90+8x^91+2x^92+4x^93+2x^95

The gray image is a code over GF(2) with n=608, k=18 and d=268.
This code was found by Heurico 1.16 in 707 seconds.