The generator matrix

 1  0  0  1  1  1 X+2  1  1  0  X  1  1  X  X  X  1  1  1  1 X+2  1  X  1  X  1  X  1 X+2  1  2 X+2  1  1  0  1  0  1  1  0  2  1  1  1  1  1  1  1  1  1  1 X+2  X X+2  1  X X+2  X  1  X  1 X+2 X+2 X+2  1  2 X+2  0  1  1 X+2  X  1  0  1  1
 0  1  0  0  1 X+1  1 X+2  3  1  X  3 X+2  1  0  1 X+1  2 X+3 X+2  1 X+1  2  2  1  3  1 X+2  1  1  2  1 X+2  2 X+2 X+3  1  X  1  1  1  X  X X+1  0 X+1 X+3  3  X X+3  0  1  1  1 X+3  1  X  0 X+2  X X+3  1  1  1  1  X  1  1 X+2  X  X  X X+1  1 X+2  0
 0  0  1  1  1  0  1  1  3  3  1  0  2  X  1 X+2  1  X X+2  1 X+1  0  1  2  0 X+3  3  3  3 X+1  1  X X+1  0  1 X+1  3 X+2 X+2  3  1 X+3  2  X X+3  1  0  1  3  2  X X+1 X+1  0  3 X+1  1  1  X  1  X  2  2  2  2  1  2 X+3 X+2 X+2  1  2  X X+2 X+2 X+2
 0  0  0  X  0  0  2  2 X+2  X  X  X  X X+2  0  0 X+2  2  0  2  0  X X+2  X X+2  2  X  X  X  2  0  2  X  0  0  2  2 X+2 X+2  X  0  X  0  2  X  2  0  X X+2 X+2  X  2  0  2 X+2 X+2  X X+2 X+2  0  0  2  0 X+2 X+2  X X+2  X X+2  0  2 X+2  X  2  0  0
 0  0  0  0  X  2  X X+2  2  2 X+2 X+2  X X+2  X X+2 X+2  X X+2  0  0  0  0  2  2  2  0  2 X+2  X  X  0 X+2  X  0  2  X  X  0 X+2 X+2  X  0  0  0  2 X+2  X X+2  X  X  X  X  0  2  X  0  2  2 X+2  0 X+2  X  0  X  X X+2  2  0 X+2 X+2  X  0 X+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+99x^68+314x^69+350x^70+552x^71+494x^72+828x^73+647x^74+744x^75+579x^76+702x^77+554x^78+592x^79+390x^80+462x^81+251x^82+254x^83+116x^84+108x^85+79x^86+30x^87+13x^88+14x^89+2x^90+2x^91+2x^92+4x^93+5x^94+2x^95+2x^96

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 4.33 seconds.