The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  X  1  X  X  1  1  1  1  X  X  1  1  1  1  1  X  X  1  1  1  1  X  2  1  1  1  1  X  1  2  2  X  1  2  1  2  1  1  2  X  1  X  1  1
 0  2  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  0  2  2  0  0  2  0  0  2  2  0  0  0  2  2  2  0  2  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  2  0  0  2  0  2  2  2  2  2  2  0  0  0
 0  0  2  0  0  0  0  0  0  0  0  0  2  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  0  0  2  0  0  2  2  2  0  0  0  2  0  2  0  0  0  2  0  2  0  0  2  2  0  2  2  2  2  2  0  2  2  2  0  2  0  2  2  0  2  2  0  0  2  0  0  0
 0  0  0  2  0  0  0  0  0  0  0  0  2  2  2  2  2  0  2  2  2  2  0  0  2  2  2  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  2  0  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0  2  2  2  0  0  2  0  0  0  2  0  0  2  0  0  2  2  0  0  0  0  0
 0  0  0  0  2  0  0  0  0  0  0  2  0  2  2  0  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  0  0  0  0  2  2  0  0  2  0  2  2  2  2  0  0  2  0  2  0  0  2  2  0  2  2  0  0  2  0  0  0  0  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  2  2  2  0  0  0  0
 0  0  0  0  0  2  0  0  0  0  0  2  0  0  2  2  2  2  2  0  0  2  2  0  0  0  2  0  0  0  2  2  0  2  2  0  2  2  2  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  2  2  0  2  2  0  0  0  0  0  2  2  0  0  0  2  0  0  2  2  2  2  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  2  0  0  0  2  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  0  0  2  2  0  2  0  2  0  0  0  2  0  0  2  0  2  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  0  0  0  2  0  2  0  2  2  2  2  2  0  0
 0  0  0  0  0  0  0  2  0  0  2  0  0  2  0  0  2  0  0  2  0  2  2  2  0  2  0  2  2  2  0  2  2  0  2  0  0  2  0  2  0  0  2  2  2  2  0  0  2  0  2  0  0  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  2  2  0  0  2  2  2  0  0  0  0  0  2  0  0  2  0  0
 0  0  0  0  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  2  0  2  0  0  2  0  0  2  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  2  2  2  0  2  2  0  0  0  0  2  2  2  0  2  2  2  2  0  0  0  0  0  0  0  2  2  0  0  0  0  0
 0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  2  0  2  2  2  2  0  2  0  2  2  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  0  0  0  2  2  0  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  0  2  0  2  2  2  0  0  0  0  0  2  0  2  0  0  0

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+64x^72+4x^74+167x^76+54x^78+292x^80+312x^82+794x^84+804x^86+804x^88+300x^90+207x^92+54x^94+110x^96+8x^98+63x^100+38x^104+16x^108+3x^112+1x^132

The gray image is a code over GF(2) with n=344, k=12 and d=144.
This code was found by Heurico 1.16 in 2.82 seconds.