The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+248x^74+160x^75+210x^76+160x^77+232x^78+10x^80+1x^84+1x^96+1x^116

The gray image is a code over GF(2) with n=608, k=10 and d=296.
This code was found by Heurico 1.16 in 0.297 seconds.