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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+105x^72+239x^76+30x^78+354x^80+146x^82+813x^84+1340x^86+2179x^88+1396x^90+779x^92+134x^94+292x^96+26x^98+199x^100+100x^104+45x^108+9x^112+4x^116+1x^140

The gray image is a code over GF(2) with n=352, k=13 and d=144.
This code was found by Heurico 1.16 in 11.4 seconds.