The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+527x^72+368x^73+612x^74+272x^75+600x^76+288x^77+640x^78+336x^79+345x^80+16x^81+60x^82+14x^84+5x^88+10x^92+2x^104

The gray image is a code over GF(2) with n=608, k=12 and d=288.
This code was found by Heurico 1.16 in 71.9 seconds.