The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+369x^68+730x^70+828x^72+606x^74+644x^76+378x^78+308x^80+124x^82+70x^84+16x^86+15x^88+2x^90+5x^92

The gray image is a code over GF(2) with n=296, k=12 and d=136.
This code was found by Heurico 1.16 in 4.79 seconds.