The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 66.

Homogenous weight enumerator: w(x)=1x^0+119x^66+116x^67+224x^68+154x^69+235x^70+138x^71+205x^72+130x^73+225x^74+112x^75+102x^76+90x^77+107x^78+18x^79+34x^80+12x^82+4x^84+8x^85+2x^86+6x^88+2x^89+2x^90+1x^94+1x^102

The gray image is a code over GF(2) with n=288, k=11 and d=132.
This code was found by Heurico 1.16 in 0.462 seconds.