The generator matrix

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

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+66x^68+270x^69+465x^70+524x^71+634x^72+704x^73+638x^74+672x^75+712x^76+708x^77+549x^78+422x^79+456x^80+378x^81+312x^82+246x^83+150x^84+118x^85+80x^86+38x^87+27x^88+10x^89+4x^90+2x^91+2x^92+4x^93

The gray image is a code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 3.28 seconds.