The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+105x^72+436x^73+840x^74+1170x^75+1497x^76+1814x^77+1999x^78+2236x^79+2340x^80+2736x^81+2725x^82+2506x^83+2635x^84+2276x^85+2034x^86+1518x^87+1250x^88+1044x^89+630x^90+432x^91+238x^92+166x^93+55x^94+38x^95+26x^96+8x^97+5x^98+4x^99+2x^100+2x^104

The gray image is a code over GF(2) with n=328, k=15 and d=144.
This code was found by Heurico 1.13 in 20.7 seconds.