The generator matrix

 1  0  1  1  1 X+2  1  1  0 X+2  1  1  1  2  1  1  X  1  1  1  2  1  X  1  1  1  X  1  X X+2  1  1  X  0  0  1  1  1  1  2  1  1  1  1 X+2  X  1  1  X  1 X+2  1 X+2  1  1  1  0  2  1  1  1  X  1  0  2  1 X+2  1  1  1  1  1  1 X+2  2  1
 0  1  1  0  1  1  X X+3  1  1 X+3 X+2  1  1  0  X  1  3  2 X+1  1  X  1  1 X+3 X+2  1  2  1  1  1  X  1  1  1  3  2  1  3  1 X+2 X+3  X  2  1  1  1  1  1 X+3  1 X+2  1  2 X+3  0  1  1  2 X+3  X  1  0  1  X  1  1  0  1  3 X+2 X+3  0  1  1  2
 0  0  X  0  0  0  0  0  0  2  0  0  2  2  0  0  2  2  2  0  2  0  0 X+2 X+2  X  X  X X+2  X X+2  X  X  X X+2  2 X+2 X+2  X  X  2  X X+2 X+2  X  X  X  X X+2  X  2 X+2  2 X+2  X  X  X X+2 X+2  2  2  2  0  X X+2 X+2  2  X  0  X  2  X  0 X+2  2  X
 0  0  0  X  0  0  X  2  X X+2  X  2 X+2  X  X  2  0  X  0  0  2 X+2  X X+2 X+2  X  2  2 X+2  0  X  2 X+2  0  0  2  X  2  2  X  X X+2 X+2  0  X  2  X  0  X  X  0  0 X+2  X  0  X X+2 X+2  X X+2  2 X+2  2  0 X+2 X+2  X  0  0  X  2  2  2  0 X+2  X
 0  0  0  0  X  0  0  X  X X+2  2  2  2  2 X+2 X+2  X X+2  X  2  X  X  0  X X+2  0  0  2  0  X  2  0 X+2  X  0  0  X X+2  2  2  0  0  0 X+2 X+2  X  2  2  0 X+2  X X+2  X  2 X+2  0  0 X+2 X+2  0  2  0  2 X+2 X+2  X X+2  X X+2 X+2 X+2  X  0  2  2  X
 0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  0  2  0  2  2  2  0  0  2  2  0  0  0  0  2  2  2  2  2  0  2  2  2  2  2  2  0  2  0  0  0  0  0  0  2  0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  0  0  0  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+54x^67+148x^68+222x^69+367x^70+474x^71+560x^72+644x^73+661x^74+740x^75+725x^76+680x^77+635x^78+570x^79+527x^80+422x^81+251x^82+160x^83+122x^84+60x^85+58x^86+32x^87+18x^88+14x^89+12x^90+14x^91+8x^92+6x^93+4x^95+1x^96+1x^100+1x^104

The gray image is a code over GF(2) with n=304, k=13 and d=134.
This code was found by Heurico 1.16 in 5.59 seconds.