The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+126x^67+369x^68+378x^69+931x^70+730x^71+1426x^72+888x^73+1594x^74+972x^75+1811x^76+1056x^77+1555x^78+890x^79+1276x^80+590x^81+768x^82+288x^83+315x^84+124x^85+129x^86+60x^87+38x^88+26x^89+14x^90+6x^91+9x^92+10x^93+1x^94+3x^96

The gray image is a code over GF(2) with n=304, k=14 and d=134.
This code was found by Heurico 1.16 in 15.3 seconds.