The generator matrix

 1  0  0  1  1  1  0  1 X+2  X  1  X  1  1  1  X  2  1  1 X+2  1  1  2  0  1  1  1 X+2  1  1  1 X+2 X+2  X  2  1  1  1  2  1 X+2  1  1  0  2  0  1  0  1  1  1  2  1  1  1  0  1  1 X+2 X+2  1  2  0  2  0  2  1  1  1  0 X+2  X  X  X
 0  1  0  0  1  1  1  X  1 X+2 X+2  1  3  3  X  1  X X+3 X+1  1  X  0  1  1  2  1  X  2 X+3 X+1  2  0  1  1  1  2  1  2  1  0  1  3 X+2  0  1  X  X  1  3 X+1  1  0 X+2 X+1  1  X X+2  1  0  X X+2  1  1  1  X  1 X+3  X  2  2  X X+2  1  X
 0  0  1 X+1 X+3  0 X+1  3  2  1  0  1  1 X+2 X+3  X  1  2  1 X+3 X+2  3  1  X X+1  1  X  1  X X+1 X+2  1 X+3 X+2 X+3 X+2  X  3  3  1  0  0  0  1  X  1 X+1 X+1  1  3  X  1 X+2  3 X+2  1 X+2  3  1  1  1  X X+3 X+1  1 X+3  0  1 X+1  1  1  1 X+2  X
 0  0  0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  2  2  0  2  2  2  2  0  2  0  0  0  2  2  2  0  0  0  2  0  0  0  2  2  2  0
 0  0  0  0  2  0  2  2  0  2  2  0  0  2  0  2  2  2  2  0  0  2  2  2  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  2  2  2  0  0  0  0  2  0  0  2  0  2  0  0  0  0  2  2  0  0  0  2  0  2  2  0  0  2  2  2  2  0  0  0
 0  0  0  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  0  2  0  2  2  2  0  0  0  0  2  2  2  2  2  2  0  0  2  0  0  0  2  0  2  2  2  0  2  2  0  0  0  2  0  2  0  2  0  0  2  0  2  0  2  2  0  0  0  2  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+403x^68+637x^70+900x^72+672x^74+565x^76+356x^78+277x^80+166x^82+85x^84+23x^86+6x^88+2x^90+3x^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 5.29 seconds.