The generator matrix

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

generates a code of length 72 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+270x^64+68x^65+540x^66+208x^67+831x^68+372x^69+1020x^70+360x^71+1032x^72+428x^73+953x^74+320x^75+715x^76+220x^77+407x^78+72x^79+226x^80+61x^82+46x^84+25x^86+9x^88+2x^90+4x^92+2x^96

The gray image is a code over GF(2) with n=288, k=13 and d=128.
This code was found by Heurico 1.16 in 7.16 seconds.