The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+128x^71+309x^72+414x^73+554x^74+496x^75+530x^76+382x^77+517x^78+316x^79+168x^80+152x^81+72x^82+18x^83+14x^84+10x^85+3x^86+1x^88+1x^90+2x^91+4x^94+1x^96+2x^97+1x^98

The gray image is a code over GF(2) with n=608, k=12 and d=284.
This code was found by Heurico 1.16 in 0.688 seconds.