The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+48x^68+152x^69+177x^70+234x^71+299x^72+360x^73+352x^74+330x^75+371x^76+348x^77+328x^78+214x^79+247x^80+248x^81+129x^82+98x^83+45x^84+30x^85+24x^86+10x^87+8x^88+12x^89+10x^90+8x^91+4x^92+2x^93+3x^94+2x^95+1x^96+1x^106

The gray image is a code over GF(2) with n=304, k=12 and d=136.
This code was found by Heurico 1.16 in 1.28 seconds.