The generator matrix

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

generates a code of length 74 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+50x^72+64x^73+24x^74+64x^75+38x^76+8x^78+3x^80+2x^84+2x^88

The gray image is a code over GF(2) with n=296, k=8 and d=144.
This code was found by Heurico 1.16 in 0.191 seconds.